POCKET  COMPANION 

,  OF 

USEFUL   INFORMATION 


APPERTAINING    TO^THEXUSE    OF 


PITTSBURGH,  PA. 

FOR 

ENGINEERS,  ARCHITECTS  AND  BUILDERS, 

BY 

C.  L.  STROBEL,  C.  E. 

M.A.S.  C.  E. 


Electrotype  Edition,  Price  $1.SO. 


WM.   G.  JOHNSTON  &  CO.   PRINT.  PITTSBURGH. 


Entered  according  to  Act  of  Congress,  in  the  year  1881,  by 

CARNEGIE  BROS.  &  CO.  LIMITED, 
In  the  Office  of  the  Librarian  of  Congress,  at  Washington. 


S3- 


PREFACE. 


THE  present  electrotype  edition  of  the  Pocket  Companion  is 
a  new  work  throughout.  It  is  intended  to  supply  such  special 
information  and  tables  as,  it  was  thought,  would  prove  valuable 
to  workers  in  wrought  iron  in  general,  and  the  patrons  of 
the  publishers,  the  firm  of  Carnegie  Bros.  &  Co.,  Limited,  in 
particular. 

The  tables,  with  a  few  exceptions,  were  computed  expressly 
for  this  work,  and  some  of  them  are  original  in  both  matter  and 
form. 

The  author  hopes  that  they  will  be  found  to  possess  the 
qualities  of  accuracy  and  reliability. 

Such  of  the  tables  a$  were  not  Calculated  for  this  work  were 
obtained  from  two  or  more  works  of  presumably  independent 
origin,  which  were  compared  for  the  detection  of  errors. 

The  table  of  weight  of  a  cubic  foot  of  substances  was  derived 
mostly  from  Trautwine,  while  for  the  table  of  linear  expansion 
of  .substances  by  heat,  Rankine  is  authority. 

The  list  of  shapes  rolled  by  the  Union  Iron  Mills  will  be  found 
increased  in  number,  and  some  of  the  sections  improved  in 
form.  All  angle  irons  are  now  made  with  flanges  of  uniform 
thickness ;  the  range  between  the  minimum  and  maximum 
weight  for  a  number  of  the  shapes  has  been  increased,  and  a  new 
and  more  rational  system  of  numbering  adopted. 


CONTENTS. 


PAGE. 
Lithographed  Sections  of  Eyebeams, 

Shapes  Nos.  1  to  13 1-4 

"  Sections  of  Deck  Beams, 

Shapes  Nos.  20  to  22 4 

"  Sections  of  Channel  Bars, 

Shapes  Nos.  25  to  45 5-8 

"  Section  of  Car  Truck  Channel, 

Shape  No.  46 8 

"  Sections  of  Angles  with  Equal  Legs, 

Shapes  Nos.  50  to  63 9 

•  "  Sections  of  Angles  with  Unequal  Legs, 

Shapes  Nos.  65  to  76 10 

"  Sections  of  Square  Root  Angles, 

Shapes  Nos.  80  to-93 .11 

"  Sections  of  Cover  Angles, 

Shapes  95  and  96 .  .12 

"  Section  of  Obtuse  Angles, 

Shape  No.  98 12 

"  Sections  of  Star  Irons, 

Shapes  Nos.  100  to  105 12 

"  Sections  of  Keystone  Octagon  Columns, 

Shapes  Nos.  110  to  113 13 

"  Sections  of  Piper's  Patent  Rivetless  Columns, 

Shapes  Nos.  115  to  118 14 

"  Sections  of  Corrugated  Columns, 

Shapes  Nos.  120  and  121 15 


Lithographed  Sections  of  Patent  Post  Irons,  PAGE. 

Shapes  Nos.  125  and  126 15 

"  Sections  of  Half  T's 

Shapes  Nos.  127  and  128 15 

"  Sections  of  T  Irons, 

Shapes  Nos.  130  to  178 16-20 

"  Section  of  Roof  Iron, 

Shape  No.  180 20 

"  Sections  of  Hand  Rails, 

Shapes  Nos.  195  and  196 21 

Sections  of  Grooved  Irons, 

Shapes  Nos.  200  to  209 21 

Sections  of  Sash  Irons, 

Shapes  Nos.  215  to  221 22 

"  Sections  of  Fence  Irons, 

Shapes  Nos.  225  to  227 22 

"  Section  of  Beveled  Flat, 

Shape  No.  230 22 

"  Sections  of  Ice  Slides, 

Shapes  Nos.  231  and  232 '. .22 

Section  of  Dove  Tail, 

Shape  No.  233 22 

"  Section  of  Z  Iron, 

Shape  No.  235 22 

"  Illustrations  of  Beams  and  their  connections, 

and   Girders 23 

"              Illustrations  of  Beam  supporting  Wall,  of  Sepa- 
rators, and  of  Fire-proof  Floors 24 

"              Illustrations  of  Fire-proof  and  other  Floors. . .  .25 
"                        "            "   Columns  and  Struts,   and  Dia- 
grams of  Pratt  and  Whipple  Trusses 26 

"  Sections  of  Additional  Shapes 27-30 

Explanation  of  Tables  on  Eyebeams 31,  32 

~~y[      "—  -£ 


PAGE. 

Tables   on   Eyebeams,  giving  Safe  Load,    Deflection  and 

Proper  Spacing 33-35 

Explanation  of  Tables  on  the  Properties  of  Beams,  Chan- 
nels, Angles,  Stars  and  Tees,  also   General  Formulae 

on  the  Flexure  of  Beams. 56-61 

Properties  of  Eye  and  Deck  Beams 62,  63 

"    Channel  Bars 64,  65 

"  "    Angle  Irons 66,  67 

Angle  Irons,  weights   corresponding  to  thicknesses  varying 

by  TV' 68 

Properties  of  T  Irons 69 

"  "    Star  Irons 69 

Explanation  of  Table  on  Riveted  Girders 70,  71 

Table  on  Riveted  Girders 72 

Explanation  of  Tables  on  Columns  and  Struts 73-76 

Keystone  Octagon  Columns,  Thicknesses  and  corresponding 

Areas  and  Weights  per  foot 77 

Piper's  Patent  Rivetless  Columns,  Thicknesses  and  correspond- 
ing Areas  and  Weights  per  foot .78 

Ultimate  Strength  of  Cast  and  Wrought  Iron  Columns 79 

"  "  Wrought  Iron  Columns 80 

Rectangular  Timber  Pillars 81 

General  Notes  on  Floors  and  Roofs 82-84 

Corrugated  and  Galvanized  Iron .' 85,  86 

Illustration  of  Application  of  Tables  on  Flat  Rolled  Iron, 
and  Decimal  Parts  of  a  Foot  for  each  ^jth  of  an  inch. .  .87 

Weights  of  Flat  Rolled  Iron  per  Lineal  Foot.  1 88-93 

Areas  of  Flat  Rolled  Iron 94-99 

Decimal  Parts  of  a  Foot  for  each  ^  of  an  inch 100-103 

Weights  and  Areas  of  Square  and  Round  Bars  of  Wrought 

Iron,  and  Circumferences  of  Round  Bars 104-109 

Sheet  Iron,  by  Birmingham  Gauge 110 

"  "      American  "     , Ill 

VII 


PAGE. 

Areas  and  Circumferences  of  Circles 112-124 

Weights  of  Rivets  and   Round-headed  Bolts 125 

Upset  Screw  Ends  for  Round  and  Square  Bars 126,  127 

Standard  Screw  Threads,  Nuts  and  Bolt  Heads,  by  Franklin- 
Institute  Standard 128 

Whitworth's  Standard  Screw  Thread 129 

Wood  Screws,  Tacks  and  Wrought  Spikes 129 

Sizes  and  Weights  of  Hot  Pressed  Square  Nuts 130 

"  "  «  Hexagon  Nuts 131 

Wrought  Iron  Welded  Tubes,  for  Gas,  Steam  or  Water 132 

Explanation  of  Tables  on  Rivets  and  Pins 133,  134 

Shearing  and  Bearing  Value  of  Rivets 135 

Maximum  Bending  Moments  to  be  allowed  on  Pins 136 

Bearing  Value  of  Pins 137 

Wooden  Beams,  Safe  Load  for 138 

Explanation  of  Tables  on  Maximum  Stresses  in  Pratt  and 

Whipple  Trusses. 139,  140 

Maximum  Stresses  in  Pratt  or  Single  Quadrangular  Trusses . .  141 
"  "  Whipple  or  Double  Quadrangular 

Trusses 142,  143 

Natural  Sines,  Tangents  and  Secants 144-152 

Logarithms  of  Numbers 153-155 

Weight  of  a  Cubic  Foot  of  Substances 156-158 

Window  Glass,  No.  of  Lights  per  Box 159 

Linear  Expansion  of  Substances  by  Heat .160 

Mensuration 161-163 

Weights  and  Measures,  United  States  and  British 164,  165 

Comparative  Tables  of  United  States  and  French,  and 

French  and  United  States  Measures 166,  167 

Strength  of  Materials 168-170 

Decimals  of  an  Inch  for  each  J?th 171 

Index 172-177 

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EXPLANATION  OP  TABLES  ON  UNION 
IRON  MILLS'  EYEBEAMS. 

Pages    33   to    55,    inclusive. 

These  tables  are  calculated  for  the  lightest  and  heaviest  weights 
to  which  each  shape  or  size  can  be  rolled,  the  term  shape  being 
meant  to  include  the  variable  sections  which  are  rolled  in  the 
same  grooves  by  increasing  or  reducing  the  distance  between  the 
rolls.  Each  shape  is  designated  by  a  single  number. 

These  tables  give : 

I.  In  second  column,  the  load  which  a  beam  will  carry  safely, 
distributed  uniformly  over  its  length,  for  the  distances  between 
supports,  (or  lengths  of  span,)  given  in  first  column ; 

II.  In  fifth  to  eleventh  columns  inclusive,  the  distances  be- 
tween centers  at  which  beams  should  be  placed  in  floors,  to  carry 
safely  loads  of  100,  125,  150,  175,  200,  250  and  300  Ibs.  per  square 
foot  (including  the  weight  of  the  beams),  for  the  distances  between 
supports  given  in  first  column ; 

III.  In  third  column,  the  deflection  of  the  beams  at  center 
under  these  loads. 

IV.  In  fourth  column,  the  weight  of  the  beam  itself,  for  a 
length  equal  to  the  distance  between  supports. 

To  determine  the  load  which  a  beam  will  carry  exclusive  of 
its  own  weight,  the  figures  in  fourth  column  must  be  subtracted 
from  the  figures  in  second  column. 

It  is  assumed  in  these  tables  that  proper  provision  is  made  for 
preventing  the  compression  flanges  of  the  beams  from  deflecting 
sideways.  They  should  be  held  in  position  at  distances  not 
exceeding  twenty  times  the  width  of  flange,  otherwise  the 
strain  allowed  should  be  reduced. 

If  the  deflection  of  beams  carrying  plastered  ceilings  exceeds 
¥!^th  of  the  distance  between  supports,  or  J^th  of  an  inch  per 
foot  of  this  distance,  there  is  danger  of  the  ceiling  cracking,  as 
has  been  found  by  practical  tests.  This  limit  is  indicated  in  the 
following  tables  by  a  cross  line,  beyond  which  the  spans  and 
loads  must  not  be  used  for  beams  intended  to  carry  plastered 
ceilings.  It  may  generally  be  assumed,  both  for  rolled  and 

m —  — a 


SB- 


built  beams,  that  the  above  limit  is  not  exceeded  so  long  as  the 
depth  of  beam  is  not  greater  than  2]fth  of  the  distance  between 
supports,  or  j£  inch  per  foot  of  this  distance. 

Inasmuch  as  the  carrying  capacity  of  beams  increases  largely 
with  their  depth,  and  it  is  therefore  economical  to  use  the  greatest 
depth  of  beam  consistent  with  the  other  conditions  to  which  it  is 
necessary  to  conform,  (as  clear  hight,  etc.,)  the  above  cases  of 
extreme  deflection  will  rarely  be  met  with  in  practice. 

EXAMPLES   OF   APPLICATION    OF   TABLES. 

I.  What  size  and  weight  of  beam  19'-G"  long  in  clear  be- 
tween walls,  and  therefore  say  20'-0"  long  between  centers  of 
supports,  will  be  required  to  carry  safely  a  uniformly  distributed 
load  of  15  tons,  the  weight  of  the  beam  included  ?  . 

Answer  :  A  15"  beam,  No.  1,  heavy,  65  Ibs.  per  foot,  will  be 
sufficient,  since  the  safe  load,  as  per  table,  for  20;  length ,=  16.38 1. 

It  is  evident,  however,  that  a  beam  intermediate  in  weight 
between  50  Ibs.  and  65  Ibs.  can  be  used,  to  ascertain  which, 
proceed  as  follows : 

The  safe  load  for  a  15"  beam  50  Ibs.  per  foot  =  14.12 t.  Since 
therefore  an  increase  in  the  carrying  capacity  of  beam,  of  2.26 1., 
(16.38 1.  —  14.12 1.,)  requires  an  increase  of  its  weight  of  15  Ibs., 
(65  Ibs.  —  50  Ibs.,)  therefore  an  increase  of  its  carrying  capacity 
of  0.88  t.,  (15t.  —  14.12  t.,)  will  require  -||j-  X  15  =  6  Ibs. 
increase  of  weight  of  beam.,  i.  e.,  the  beam  should  weigh  56  Ibs. 
per  foot. 

II.  A  fire-proof  floor  24'-6"  in  clear  between  walls,  weighing, 
inclusive  of  beams,  70  Ibs.  per  square  foot,  (assumed,)  is  to  be 
proportioned  to  carry  an  additional  load  of  130  Ibs.  per  square 
foot;    what  size  and  weight  of  beams  will  be  required,  and  how 
far  apart  should  they  be  placed  ? 

Answer  :  The  total  load  =  200  Ibs.  per  square  foot,  and  the 
distance  between  supports  =  25',  z.  e.  6"  greater  than  the  distance 
in  clear  between  walls.  By  referring  to  tables,  it  will  be  seen 
that  either  light  12"  beams  weighing  42  Ibs.  per  foot,  spaced 
2.9  ft.  between  centers,  or  light  15"  beams,  50  Ibs.,  spaced  5.8  ft. 
between  centers,  will  answer  the  purpose,  but  since  the  12" 
beams  for  this  span  and  load  are  beyond  the  cross-line,  they 
must  not  be  used,  if  intended  to  carry  a  plastered  ceiling. 
_  ,  _ 


•S3 


UNION     IRON     MILLS' 

15-INCH    EYEBEAM,  No. 

1,  LIGHT, 

50 

LBS.  PER  FOOT. 

Depth,  15".     Width  of  Flanges,  5.03". 

Thickness  of  Web,  0.47". 

Maximum  fiber 

strain  =  12000  1 

bs.  per  square  inch. 

g  -U 

ti^s 

J3 

la 

Proper  distance, 

in  feet,  center  to  center 

s  Js 

|lli 

jl 

i  |  J 

of  b< 

jams,  for  Safe  Loads  of 

8  5 

-JfiS 

I-S 

?5 

100 

125 

150 

175 

200 

250 

200 

§    " 

J_, 

•.§  '&' 

j    5    M 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

.s   &1 

•~-~  &o 

d-s 

!  'SPJ 

per 

per 

per 

per 

per 

per 

per 

314!.s.s 

« 

r^- 

s<i.  ft. 

sq.  ft. 

54.  ft. 

£<1.  ft. 

s<l.  ft. 

sq.  ft.  |  f  q.  ft. 

10 

28.24 

0.09 

10.25 

56.5 

45.2 

37.7 

32.3 

2si 

22.6   1S.8 

11 

25.67 

0.11 

!0.28 

46.7 

37.4 

31.1 

26.7 

23^3 

18.7   15.6 

23.53 

0.13 

10.30 

39.2 

31.4 

26.1 

22.4 

19.6 

15.7 

13.1 

13 

21.72 

0.16 

S0.33 

33.4 

26.7 

22.3 

19.1 

16.7 

13.4   11.1 

14 

20.17 

0.18 

0.35 

28.8 

23.0 

19.2 

16.5 

14.4 

11.5  j   9.6 

15 

18.83 

0.21 

0.38 

25.1 

20.1 

16.7 

14.3 

12.6 

10.0  1   8.4 

16 

17.65 

0.24 

0.40 

22.1 

17.7 

14.7 

12.6   11.0 

8.8     7.4 

17 

16.61 

0.27 

0.43 

19.5 

15.6 

13.0  !  11.1 

9.8 

7.8 

6.5 

18 

15.69 

0.30 

10.45 

17.4 

13.9 

11.6 

9.9 

8.7 

7.0 

5.8 

19 

14.86 

0.33 

0.48 

15.6 

12.5 

10.4 

8.9 

7.8 

6.2 

5.2 

20 

14.12 

0.37 

0.50 

14.1 

n.3 

9.4 

8.1 

7.1 

5.6 

4.7 

21 

13.45    0.41 

0.53 

12.8 

10.2 

8.5 

7.3 

6.4 

5.1 

4.3 

22 

12.84  !0.45 

0.55 

11.7 

9.3 

7.8 

6.7 

5.8 

4.7 

3.9 

23 

12.28 

0.49 

0.58 

10.7 

8.6 

7.1 

6.1 

5.3 

4.3 

3.6 

24 

11.77 

0.53 

0.60 

9.8 

7.8 

6.5 

5.6 

4.9 

3.9     3.3 

25 

11.30 

0.58 

0.63 

9.0 

7.2 

6.0 

5.1 

4.5 

3.6 

3.0 

26 

10.86    0.62 

0.65 

8.4 

6.7 

5.6 

4.8 

4.2 

3.4  j   2.8 

27 

10.46 

0.67 

0.68 

7.7 

6.2 

5.1 

4.4 

3.9 

3.1  i   2.6 

28 

10.09 

0.72 

0.70 

7.2 

5.8 

4.8 

4.1 

3.6 

2.9     2.4 

29 

9.74 

0.78 

0.73 

6.7 

5.4 

4.5 

3.8 

3.4 

2.7     2.2 

30 

9.41 

0.83 

0.75 

6.3 

5.0 

4.2 

3.6     3.1     2.5     2.1 

31 

9.11 

0.89 

0.78 

5.9 

4.7 

3.9 

3.4     2.9 

2.4     2.0 

32 

8.83 

0.94 

0.80 

5.5 

4.4 

3.7 

3.2     2.8 

2.2 

1.8 

33 

8.56 

1.00 

0.83 

5.2 

4.2 

3.5 

3.0     2.6 

2.1     1.7 

34 

8.31 

1.07 

0.85 

4.9 

3.9 

3.3 

2.8 

2.4 

2.0 

1.6 

35 

8.07 

1.13 

0.88 

4.6 

3.7 

3.1 

2.6 

2.3 

1.8 

1.5 

36 

7.84 

1.19 

0.90 

4.4 

3.5 

2.9 

2.5 

2.2 

1.7 

1.5 

37 

7.63 

1.26 

0.93 

4.1 

3.3 

2.7 

2.4 

2.1 

1.6 

1.4 

38 

7.43 

1.33 

0.95 

3.9 

3.1 

2.6 

2.2 

2.0 

1.6 

1.8 

39 

7.24 

1.40 

0.98 

3.7 

3.0 

2.5 

2.1 

1.9 

1.5     1.3 

•88 


UNION     IRON     MILLS' 

15-INCH    EYEBEAM,   No.   1,    HEAVY, 

65  LBS.  PER  FOOT. 

Depth,  15".    Width  of  Flanges,  5.33".    Thickness  of  Web,  0.77". 

Maximum  fiber  strain  =  12000  Ibs.  per  square  inch. 

Ja 

till 

II 

a 

g~~ 

Proper  distance,  in  feet,  center  to  center 
of  beams,  for  Safe  Loads  of 

—^ 

J  5 

55 

100 

125 

150 

175 

200 

250 

300 

ji  ^ 

S    m 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

.2    §* 

-<D  -^  ko~^    <§  .3 

'^3 

per 

per 

per 

per 

per 

p3r 

per 

IS  41  .S  .5    « 

£ 

si.  ft. 

si.  ft.    4  ft  i  si.  ft. 

£1.  ft. 

si.  ft, 

tfft. 

10 

32.76    0.09 

0.33 

65.5 

52.4 

43.7 

37.4   32.8 

26.2 

21.8 

11 

29.78  1  0.11 

0.36 

54.1 

43.3 

36.1 

30.9 

27.1   21.7 

18.0 

12 

27.30 

0.13 

0.39 

45.5 

36.4  30.3 

26.0 

22.8   18.2 

15.2 

13 

25.20 

0.16 

0.42 

33.8 

31.0  25.8 

22.2 

19.4  !  15.5 

12.9 

14 

23.40 

0.18 

0.46 

33.4 

26.7 

22.3 

19.1 

16.7   13.4 

11.1 

15 

21.84 

0.21 

0.49 

29.1 

23.3 

19.4 

16.6 

14.6   11.6 

9.7 

16 

20.48  iO.24 

0.52 

25.6 

20.5 

17.1 

14.6 

12.8 

10.2 

8.5 

17 

19.27    0.27 

0.55 

22.7 

18.1 

15.1 

13.0 

11.3 

9.1 

7.6 

18 

18.20    0.30- 

0.59 

20.2 

16.2 

13.5 

11.6 

10.1 

8.1  1   6.7 

19 

17.24    0.33 

0.62 

18.1 

14.5 

12.1 

10.4 

9.1 

7.3     6.0 

20 

16.38 

0.37 

0.65 

16.4 

13.1 

10.9 

9.4 

8.2 

6.6     5.5 

21 

15.60 

0.41 

0.68 

14.9 

11.9 

9.9 

8.5 

7.4     5.9  i   5.0 

22 

14.89 

0.45 

0.72 

13.5 

10.8 

9.0 

7.7 

6.8 

5.4)   4.5 

23 

14.24 

0.49 

0.75 

12.4 

9.9 

8.3 

7.1 

6.2 

5.0     4.1 

24 

13.65 

0.53 

0.78 

11.4 

9.1 

7.6 

6.5 

5.7 

4.6  1   3.8 

25 

13.10 

0.58 

O.P1 

10.5 

8.4 

7.0 

6.0    5.2. 

4.2  j   3.5 

26 

12.60 

0.62 

0.85 

9.7 

7.8 

6.5 

5.5 

4.8 

3.9  i   3.2 

27 

12.13 

0.67  0.88 

9.0 

7.2 

6.0 

5.1 

4.5 

3.6;    3.0 

28 

11.70 

0.72  1  0.91 

8.4 

6.7 

5.6 

4.8 

4.2 

3.3 

2.8 

29 

11.30 

0.78 

0.94 

7.8 

6.2 

5.2 

4.4 

3.9 

3.1 

2.6 

30 

10.92 

0.83 

0.98 

7.3 

5.8 

4.9 

4.2 

3.6 

2.9 

2.4 

31 

10.57 

0.89  i  1.01 

6.8 

5.5 

4.5 

3,9     3.4     2.7 

2.3 

32 

10.24 

0.95 

1.04 

6.4 

5.1 

4.3 

3.7 

3.2     2.6 

2.1 

33 

9.93 

1.01 

1.07 

6.0 

4.8 

4.0 

3.4 

3.0 

2.4 

2.0 

34 

9.64 

1.07 

1.11 

5.7 

4.5 

3.8 

3.2     2.8 

2.3 

1.9 

35 

9.36 

1.13 

1.14 

5.3 

4.3 

3.6 

3.1     2.7    2.1 

1.8 

33 

9.10 

1.20 

1.17 

5.1     4.0 

3.4     2.9     2.5     2,0 

1.7 

37 

8.85 

1.26 

1.20 

4.8     3.8     3.2     2.7     2.4     1.9  i    1.6 

38 

8.62 

1.33 

1.24 

4.5     3.6 

3.0 

2.6 

2.3     1.81   1.5 

39 

8.40 

1.40 

1.27 

4.3     3.4 

2.9 

2.5 

2.2 

1.7  !   1.4 

i 

!  i  c 

:<—                  — 

UNION     IRON     MILLS' 

15-INCH    EYEBEAM,   No. 

2,   LIGHT, 

67 

LBS.  PER  FOOT. 

Depth,  15".    Width  cf  Flanges,  5.55". 

Thickness  of  Web,  0.67". 

Maximum  fiber 

strain  =  12000  Ibs.  per  square  inch. 

•  g^ 

ti?^ 

3 

rt 

Proper  distance, 

in  feet,  center  to  center 

«  " 

licl 

11 

Ig 

of  b 

earns, 

forSa 

e  Loads  01 

s  i 

5ri? 

s  " 

'o'~ 

°  °o 

100 

125 

150 

175 

200 

250 

300 

.3  §. 

0,0  'S  g 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

I  i* 

s'-i  bL^ 

<i  .2 

be  § 

per 

per 

per 

per 

per 

per 

per 

3l^.2.2 

« 

£*" 

sq.  ft 

sq.ft. 

sq.  ft.    sq.  ft. 

£q.  ft. 

sq.  ft. 

sq.  ft. 

i_    —   —   — 

I 

. 

10 

36.12 

0.09 

0.34 

72.2  57.8 

48.2 

41.3 

36.1 

28.9 

24.1 

11 

32.84 

0.11 

0.37 

59.7  47.8 

39.8 

34.1 

29.9 

23.9 

19.9 

12 

30.10 

0.13 

0.40 

50.2 

40.1 

33.4 

28.7 

25.1 

20.1 

16.7 

13 

27.78 

0.16 

0.44 

42.7 

34.2 

28.5 

24.4 

21.4 

17.1 

14.2 

14 

25.80 

0.18 

0.47 

36.9 

29.5 

24.6 

21.1 

18.4 

14.7 

12.3 

15 

24.08 

0.21 

0.50 

32.1 

25.7 

21.4 

18.3 

16.1 

12.8 

10.7 

16 

22.58 

0.24 

0.54 

28.2 

22.6 

18.8 

16.1 

14.1 

11.3 

9.4 

17 

21.25 

0.27 

0.57 

25.0 

20.0 

16.7 

14.3 

12.5 

10.0 

8.3 

18 

20.07 

0.30 

0.60 

22.3 

17.8 

14.9 

12.7 

11.2 

8.9 

7.4 

19 

19.01 

0.33 

0.64 

20.0 

16.0 

13.3 

11.4 

10.0 

8.0 

6.7 

20 

18.05 

0.37 

0.67 

18.1 

14.4 

12.0 

10.3  !   9.0 

7.2 

6.0 

21 

17.20 

0.41 

0.70 

16.4 

13.1 

10.9 

9.4 

8.2 

6.6 

5.5 

22 

16.42 

0.45 

0.74 

14.9 

11.9 

10.0 

8.5 

7.5     6.0 

5.0 

23 

15.70 

.0.49 

0.77 

13.7 

10.9 

9.1 

7.8 

6.8     5.5 

4.6 

24 

15.05 

i  0.53 

0.80 

12.5   10.0 

8.4 

7.2 

6.3     5.0 

4.2 

25 

14.45 

0.58 

0.84 

11.6 

9.2 

7.7 

6.7 

5.8     4.6 

3.9 

26 

13.89 

10.62 

0.87 

10.7 

8.5 

7.1 

6.1 

5.3     4.3 

3.6 

27 

13.38 

J0.67 

0.91 

9.9     7.9 

6.6 

5.6 

5.0 

4.0 

3.3 

28 

12.90 

:0.72 

0.94 

9.2     7.4 

6.2 

5.3 

4.6 

3.7 

!  3.1 

29 

12.46 

10.78 

0.97 

8.6     6.9 

5.7 

4.9 

4.3 

3.4 

2.9 

30 

12.04 

!o.83 

1.01 

8.0 

6.4 

5.4 

4.6 

4.0 

3.2 

2.7 

31 

11.65 

!0.89 

1.04 

7.5  |.  6.0     5.0  1  4.3 

3.8 

3.0 

i  2.5 

32 

11.29 

0.95 

1.07 

7.1     5.6 

4.7 

4.0 

3.5 

2.8 

!  2.4 

33 

10.95 

1.01 

1.11 

6.6     5.3 

4.4 

3.8 

3.3 

2.7 

;  2.2 

34 

10.62 

1.07 

1.14 

6.2     5.0 

4.1 

3.6 

3.1 

2.5 

;  2.1 

35 

10.32 

1.13 

1.17' 

5.9     4.7 

3.9 

3.4 

2.9 

2.4 

2.0 

36 

10.03 

1.20 

1.21 

5.6     4.5 

3.7 

3.2 

2.8 

2.2 

1.9 

37 

9.76 

:i.26 

1.24 

5.3     4.2 

3.5 

3.0 

2.6 

2.1 

1.8 

38 

9.51 

1.33 

'1.27 

5.0     4.0 

3.3 

2.9 

2.5 

2.0 

1   1.7 

39 

9.26 

1.40 

1.31 

4.7     3.8 

3.2 

2.7 

1.9 

,   1.6 

'A  

£ 

J  — 

—  s: 

UNION     IRON     MILLS' 

15-INCH    EYEBEAM,   No.   2,   HEAVY, 

80  LBS.  PER  FOOT. 

Depth,  15".    Width  of  Flanges,  5.81".    Thickness  of  Web,  0.93". 

Maximum  fiber  strain  =  12000  Its.  per  sojiare  inch. 

•ji?*  a  * 

S3 

Proper  distance,  in  fee 

~  center  to  center 

|  <! 

jjUjlg  "fe-g 

H"s2 

of  beams,  for  Safe  Loads  of 

to     & 

a  '-^"g  H  i  13  .2 

rO    t~~-1 

§  r~ 

^  rt 

°s 

ICO       125 

0 

175 

200 

2CO 

soo 

1  a 

•3:2  1  1 

iif 

•g>3 

Us. 

Ibs. 

Its. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

•&  3 

.«      •£         Jjg"^                 ^       ,3 

'G  _g 

per 

per 

per 

per 

per 

par 

per 

tg:a.s.s  « 

^ 

ai.fi, 

El.ft    sq.ft. 

sq.  ft. 

Bl.it 

s:q.  ft. 

^.  ft  • 

10 

40.00    0.09 

0.40 

80.0 

64.0  53.3 

45.7 

40.0 

32.0 

26.7 

11 

33.36  !  0.11 

0.44 

66.1 

52.9  44.1   37.8 

33.1 

26.4 

22.0 

12 

33.33 

0.13 

0.48 

55.6 

44.4 

37.0  31.7 

27.8 

22.2 

18.5 

13 

30.77 

0.16 

0.52 

47.3 

37.9 

31.6 

27.1 

23.7 

18.9 

15.8 

14 

28.57 

0.18 

0.56 

40.3 

32.6 

27.2 

23.3 

20.4 

16.3 

13.6 

15 

28.67 

0.21 

0.60 

35.6 

28.4 

23.7 

20.3 

17.8 

14.2 

11.9 

16 

25.00 

0.24 

O.C4 

31.3 

25.0 

20.8 

17.9   15.6 

12.5 

10.4 

17 

23.53 

0.27 

O.C8 

27.7 

22.1 

18.5 

15.8  j  13.8 

11.1 

9.2 

18 

22.22 

0.30 

0.72 

24.7 

19.8 

16.5 

14.1 

12.3 

9.9!   8.2 

19 

21.05    0.33 

0.76 

22.2 

17.7 

14.8 

12.6 

11.1 

8.9 

7.4 

20 

20.00    0.37 

0.80 

20.0 

16.0 

13.3 

11.4 

10.0 

8.0 

6.7 

21 

19.05 

0.41 

0.84 

18.1 

14.5 

12.1    10.4 

9.1 

7.3 

6.0 

22 

18.18    0.45 

0.88 

16.5 

13.2 

11.0 

9.4 

8.3 

6.6 

5.5 

23 

17.39    0.49 

0.92 

15.1 

12.1 

10.1 

8.6 

7.6 

6.0 

5.0 

24 

16.67 

0.53 

0.96 

13.9 

11.1 

9.3 

7.9 

6.9 

5.6 

4.6 

25 

16.00 

0.58 

1.00 

12.8 

10.2 

8.5 

7.3 

6.4 

5.1 

4.3 

26 

15.38 

O.C2 

1.C4 

11.8 

9.5 

7.9 

6.8 

5.9 

4.7 

3.9 

27 

14.81 

0.67 

1.08 

11.0 

8.8 

7.3     6.3 

5.5 

4.4 

3.7 

23 

14.29    0.72   1.12 

10.2 

8.2     6.8!   5.8  j  5.1 

4.1 

3.4 

29 

13.79 

0.78  i  1.16 

9.5 

7.6     6.3     5.4 

4.8 

3.8 

3.2 

30 

13.33 

0.83   1.20 

8.9 

7.1     5.9     5.1 

4.4 

3.6 

3.0 

31 

12.90 

0.89   1.24 

8.3 

6.6'  5.5     4.8 

4.2 

3.3 

2.8 

32 

12.50    0.9511.28 

7.8 

6.2     5.2  ;   4.5 

3.9 

3.1 

2.6 

83 

12.12    1.01   1.82 

7.3 

5.9^   4.9     4.2 

3.7 

2.9 

2.4 

84 

11.76  !  1.07  1.36 

6.9     5.5;  4.6;   3.9 

3.5 

2.8 

2.3 

35 

11.43    1.13  1.40 

6.5     5.2  '   4.3     3.7 

3.3 

2.6 

2.2 

86 

11.11    1.20   1.44 

6.2    4.9;  4.1     3.5 

3.1 

2.5 

2.1 

37 

10.81    1.26  1.43 

5.8;  4.7     3.9,   3.3 

2.9 

2.3 

1.9  ' 

38 

10.68 

1.33  !  1.52 

5.5  i   4.4 

3.7     3.2 

2.8 

2.2 

1.8 

39 

'4 

10.28    1.40  1.56 

5.3     4.2 

3.5     3.0 

2.6'  i  2.1 

1.8 
c 

•• 

f. 

UNION    IRON    MILLS1 

12-INCH    EYEBEAM,   No.   3,   LIGHT, 

42 

LBS.  PER  FOOT. 

Depth,  12".    Width  of  Flanges,  4.64".    Thickness  of  Web,  0.51". 

Maximum  fiber  strain  =  12000  Ibs.  per  square  inch. 

CJ    +3 

li^s 

1   o3 

a 

Proper  distance,  in  feet,  center  to  center 

{I 

t.  ^0     33 

|1 

JS 

of  beams,  for  Safe  Loads  of 

fi   ^ 

f=g 

°°  <*-! 

100 

125   1    150       175       200 

250 

300 

| 

15 

ili 

Ibs. 

Ibs.       Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

a  & 

If 

A 

per 
sq.  ft. 

par 
sq.  ft. 

per 
sq.  ft. 

per 

sq.ft. 

per 
sq.ft. 

per 
sjft. 

10 

18.36 

0.12 

0.21 

36.7  29.4 

24.5 

21.0 

18.4 

14.7 

12.2 

11 

16.69 

0.14 

0.23 

30.3 

24.3 

20.2 

17.3 

15.2 

12.1 

10.1 

12 

15.30 

0.17 

0.25» 

25.5 

20.4 

17.0 

14.6 

12.8 

10.2 

8.5 

13 

14.12 

0.20 

0.27 

21.7 

17.4 

14.5 

12.4 

10.9 

8.7 

7.2 

14 

13.11  J0.23 

0.29 

18.7 

15.0 

12.5   10.7 

9.4 

7.5 

6.2 

15 

12.24 

0.26 

0.32 

16.3 

13.1 

10.9 

9.3 

8.2 

6.5 

5.4 

16 

11.48 

0.30 

0.34 

14.4 

11.5 

9.6 

8.2 

7.2 

5.7 

4.8 

17 

10.80 

0.33 

0.36 

12.7 

10.2 

8.5 

7.3 

6.4 

5.1 

4.2 

18 

10.20  i  0.37 

0.38 

11.3 

9.1 

7.6 

6.5 

5.7 

4.5 

3.8 

19 

9.66    0.42 

0.40 

10.2 

8.1 

6.8 

5.8 

5.1 

4.1 

3.4 

20 

9.18 

0.46 

0.42 

9.2 

7.3 

6.1 

5.2 

4.6 

3.7 

3.1 

21 

8.74 

0.51 

0.44 

8.3 

6.7 

5.5 

4.8 

4.2 

3.3 

2.8 

22 

8.35 

0.56 

0.46 

7.6 

6.1 

5.0 

4.3 

3.8 

3.0 

2.5 

23 

7.98 

0.61 

0.48 

6.9 

5.6 

4.6 

4.0 

3.5 

2.8 

2.3 

24 

7.65 

0.68 

0.50 

6.4 

5.1 

4.2 

3.6 

3.2 

2.6 

2.1 

25 

7.34 

0.72" 

0.53 

5.9 

4.7  1   3.9 

3.3 

2.9 

2.4 

2.0 

26 

7.06 

0.78 

0.55 

5.4 

4.3     3.6 

3.1 

2.7 

2.2 

1.8 

27 

6.80 

0.84 

0.57 

5.0 

4.0     3.3 

2.9 

2.5 

2.0 

1.7 

28 

6.56 

0.90 

0.59 

4.7 

3.7 

3.1 

2.7 

2.3 

1.9 

1.6 

29 

6.33 

0.97 

0.61 

4.4 

3.5 

2.9 

2.5 

2.2 

1.7 

1.5 

30 

6.12 

1.04 

0.63 

4.1 

3.3 

2.7 

2.3 

2.0 

1.6 

1.4 

31 

5.92 

1.11 

0.65 

3.8 

3.1 

2.5     2.2 

1.9 

1.5 

1.3 

32 

5.74 

1.18 

0.67 

3.6 

2.9 

2.3     2.0 

1.8 

1.4 

1.2 

33 

5.56 

1.26 

0.69 

3.4 

2.7 

2.2 

1.9 

1.7 

1.3 

1.1 

34 

5.40 

1.34 

0,71 

3.2 

2.5 

2.1 

1.8 

i.6 

1.3 

1.1 

35 

5.25 

1.42 

0.74 

3.0 

2.4 

2.0 

1.7 

1.5 

1.2 

1.0 

36 

5.10 

1.50 

0.76 

2.8 

2.2 

1.9 

1.6 

1.4 

1.1 

0.9 

37 

4.96 

1.58 

0.78 

2.6    2.1 

1.8 

1.5 

1.3 

1.1 

0.9 

38 

4.83 

1.67 

0.80 

2.5     2.0 

1.7 

1.5 

1.3 

1.0 

0.8 

39 
5r~~  

4.71 

1.76 

0.82 

2.4 

1.9 

1.6 

1.4 

1.2 

1.0 

0.8 

5  — 

—  E 

UNION     IRON     MILLS' 

12-INCH    EYEBEAM,   No. 

3,   HEAVY, 

60  LBS.  PER  FOOT. 

Depth,  12".    Width  of  Flanges,  5.09".    Thickness  of  Web,  0.96". 

Maximum  fiber  strain  =  12000  Ibs.  per  square  inch. 

rt  *» 

||  P  1  . 

2 

Proper  distance, 

in  feet,  center  to  center 

|  J 

bl 

fs 

of  beams, 

for  Safe  Loads  of 

2  •  J 

I'-^si  1-2 

1 

§  -|2 

"."3  ,3  =«    ^  2 

°«~ 

100 

125 

150 

175 

200 

250 

300 

jf  §« 

-ill  If 

-*»  ° 

-a    01 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

•a  1 

JI.2.S   1 

ll 

per 
rq.  ft. 

per 

sq.  ft. 

per 
sq.ft. 

per 

sq.  ft. 

per 

sq.ft. 

per 
sq.ft. 

per 
sq.ft. 

10 

22.68    0.12 

0.30 

45.4   36.3 

30.2 

25.9 

22,7 

18.1 

15.1 

11 

20.62 

0.14   0.33 

37.5 

30.0.  25.0 

21.4 

18.7 

15.0 

12.5 

12 

18.90    0.17  0.36 

31.5 

25.21  21.0 

18.0 

15.8 

12.6 

10.5 

13 

17.45 

0.20  |  0.39 

26.8 

21.5  i  17.9 

15.3 

13.4 

10.7 

8.9 

14 

16.20 

0.23   0.42 

23.1 

18.5  i  15.4 

13.2 

11.6 

9.3 

7.7 

15 

15.12 

0.26  !  0.45 

20.2 

16.1  '  13.4 

11.5 

10.1 

8.1 

6.7 

16 

14.18 

0.30  1  0.48 

17.7 

14.2  !  11.8 

10.1 

8.9     7.1 

5.9 

17 

13.34 

0.33  !  0.51 

15.7 

12.6   10.5 

9.0 

7.8     6.3 

5.2 

18 

12.60 

0.37   0.54 

14.0 

11.2  i  9.3 

8.0 

7.0 

5.6 

4.7 

19 

11.94 

0.42  i  0.57 

12.6 

10.1     8.4 

7.2 

6.3 

5.0     4.2 

20 

11.34 

0.46   0.60 

11.3 

9.1 

7.6 

6.5 

5.7 

4.5     3.8 

21 

10.80 

0.51   0.63 

10.3 

8.2     6.9 

5.9 

5.2 

4.1 

3.4 

22 

10.31 

0.56 

0.66 

9.4     7.5     6.2 

5.4 

4.7 

3.7 

3.1 

23 

9.86 

0.61 

0.69 

8.6  i   6.9     5.7 

4.9 

4.3 

3.4 

2.9 

24 

9.45 

0.66 

0.72 

7.9 

6.3     5.3 

4.5 

3.9 

3.1 

2.6 

i 

25 

9.07 

0.72 

0.75 

7.3 

5.8 

4.9 

42 

36 

29 

2.4 

26 

8.72 

0.78 

0.78 

6.7 

5.4 

4.5 

3^9 

3^3 

27 

2.2 

27 

8.40 

0.84 

0.81 

6.2 

5.0 

4.2 

3.6 

3.1 

2.5 

2.1 

28 

8.10 

0.90   0.84 

5.8 

4.6 

3.9 

a.3 

2.9 

2.3 

1.9 

29 

7.82 

0.97  i  0.87 

5.4 

4.3 

3.6 

3.1 

2.7 

2.1 

1.8 

30 

7.56 

1.04 

0.90 

5.0     4.0 

3.4 

2.9 

2.5 

2.0 

1.7 

31 

7.32 

1.11 

0.93 

4.7 

3.8 

3.2 

2.7 

2.4 

1.9 

1.6 

32 

7.09 

1.18 

0.96 

4.4 

3.5 

3.0 

2.5 

2.2 

1.8 

1.5 

33 

6.87 

1.26 

0.99 

4.2 

3.3 

2.8 

2.4 

2,1 

1.7 

1.4 

34 

6.67 

1.34 

1.02 

3.9 

3.1 

2.6 

2.2 

2.0 

1.6 

1.3 

35 

6.48 

1.42 

1.05 

3.7 

3.0 

2.5 

2.1 

1.9 

1.5 

1.2 

36 

6.30    1.50   1.08 

3.5 

2.8 

2.3 

2.0 

1.8 

1.4 

1.2 

37 

6.13 

1.58 

1.11 

3.3 

2.6 

2.2 

1.9 

1.7 

1.3 

1.1 

38 

5.97 

1.67 

1.14 

3.1 

2.5 

2.1 

1.8 

1.6 

1.3 

1.0 

39 

5.82 

1.76 

1.17 

3.0 

2.4 

2.0 

1.7 

1.5 

1.2 

1.0 

G 

B                                                 38 

* 

—  rz 

UNION     IRON     MILLS' 

10K-INCH    EYEBEAM, 

No. 

4,  LIGHT, 

313-2 

LBS.  PER 

FOOT. 

Depth,  10K".    Width 

of  Flanges,  4.54" 

.    Thickness  of  Web,  0.41". 

Maximum  fiber 

strain  =  12000  Ibs.  per  square  inch. 

g  -g 

l^?2 

t3  „; 

A. 

Proper  dis 

>tance,  in  feet,  center  to  center 

1  3 

Ifli 

I 

of  b< 

jams,  for  Safe  Loads  of 

§  42" 

?'"o 

(S  --1 

o  .(  t 

100    '    125 

150 

175   !    200 

250 

300 

3  1 

§ 

•Ssi1 

j3  » 

Ibs.   i  Ibs. 

Ibs. 

Ibs.       Ibs. 

Ibs. 

Ibs. 

s  1* 

=2^  bD° 

<§~ 

•ifj 

per   i   per 

per 

per       per 

per 

per 

ji^.s.s 

« 

* 

sq.  ft.  j  sq.  ft. 

sq.  ft. 

sq.  ft.    sq.  ft. 

sq.ft. 

sq.  ft. 

. 

10 

12.56 

0.13 

0.16 

25.1  1  20.1 

16.7 

14.4   12.6 

10.0 

8.4 

11 

11.42 

0.16 

0.17 

20.8  i  16.6 

13.8 

11.9   10.4 

8.3 

6.9 

12 

10.47 

0.19 

0.19 

17.5   14.0 

11.6 

10.0     8.7 

7.0 

5.8 

13 

9.66 

0.22 

0.21 

14.9  1  11.9 

9.9 

8.5     7.4 

5.9 

5.0 

14 

8.97 

0.26 

0.22 

12.8  i  10,2 

8.5 

7.3     6.4 

5.1 

4.3 

15 

8.37 

0.30 

0.24 

11.2;  8.9 

7.4 

6.4:   5.6- 

4.5 

3.7 

16 

7.85 

0.34 

0.25 

9.8  i  7.8 

6.5 

5.6;   4.9 

3.9 

3.3 

17 

7.39 

0.38 

0.27 

8.7'  7.0 

5.8 

5.0     4.3 

3.5 

2.9 

18 

6.98 

0.43 

0.28 

7.8;   6.2 

5.2 

4.4     3.9 

3.1 

2.6 

19 

6.61 

0.48 

0.30 

7.0;  5.6 

4.6 

4.0     3.5 

2.8 

2.3 

20 

6.28 

0.53 

0.32 

6.3     5.0 

4.2 

3.6     3.1 

2.5 

2.1 

21 

5.98 

0.58 

0.33 

5.7     4.6 

3.8 

3.3     2.8 

2.3 

1.9 

88 

5.71 

0.64 

0.35 

5.2     4.2 

3.5 

3.0     2.6 

.2.1 

1.7 

23 

5.46 

0.70 

0.36 

4.8     3.8 

3.2 

2.7     2.4 

1.9 

1.6 

24 

5.23 

0.76 

0.38 

4.4     3.5 

2.9 

2.5     2.2 

1.7 

1.5 

25 

5.02 

0.82 

0.39 

4.0     3.2 

2.7 

2.3     2.0 

1.6 

1.3 

26 

4.83 

0.89 

0.41 

3.7     3.0 

2.5 

2.1     1.9 

1.5 

1.2 

27 

4.65 

0.96 

0.43 

3.4     2.8 

2.3 

2.0     1.7 

1.4 

1.1 

28 

4.49 

1.03 

0.44 

3.2;   2.6 

2.1 

1.8     1.6 

1.3     1.1 

29 

4.33 

1.11 

0.46 

3.0;   2.4 

2.0 

1.7;   1.5 

1.2 

1.0 

30 

4.19 

1.19 

0.47 

2.8'   2.2 

1.9 

1,6:   1.4 

1.1 

.9 

31 

4.05 

1.27 

0.49 

2.6;   2.1 

1.7 

1.5     1.3 

1.0 

.9 

32 

3.93 

1.35 

0.50 

2.5     2.0 

1.6 

1.4     1.2 

1.0 

.8 

33 

3.81 

1.44 

0.52 

2.3     1.8 

1.5 

1.3!   1.2 

.9 

.8 

34 

3.69 

1.53 

0.54 

2.2;    1.7 

1.4 

1.2     1.1 

.9 

.7 

35 

3.59 

1.62 

0.55 

2.1     1.6 

1.4 

1.2     1.0 

.8 

7 

36 

3.49 

1.71 

0.57 

1.9;   1.6 

1.3 

1.1     1.0 

.8 

.6 

37 

3.39 

1.80 

0.58 

1.8     1.5 

1.2 

1.1  !     .9 

.7 

.6 

38 

3.31 

1.90 

0.60 

1.7;    1.4 

1.2 

1.0  ,     .9 

.7 

.6 

39 

'4  

3.22 

2.01 

0.61 

1.7!   1.3 

1.1 

.9;     .8 

.7      .6 

H 

UNION     IRON     MILLS' 

10^-INCH    EYEBEAM,   No. 

4,   HEAVY, 

45  LBS.  PER  FOOT. 

Depth,  10}^".    Width  of  Flanges, 

4.92".    Thickness  of  Web,  0.79". 

Maximum  fiber  strain  =  12000  Ibs.  pe 

r  square  inch. 

a  ^ 

ti^s 

1.9        !    ft 

i  ^  „-  i  ••:.-• 

Proper  distance, 

in  feet,  center  to  center 

11 

jj'gj^g 

of  beams,  for  Safe  Loads  of 

i* 

if 

Jit's 

1  a  •**      °  <*-. 

175 

100 

125       ICO 

200 

250 

300 

§       0 

*8fj|lf  Hi 

Ibs. 

Ibs.    :   Ibs. 

Ibs. 

Ibs. 

Its. 

Ibs. 

Q     w 

iirfr  I1 

per 
apt 

per       per 
sq.  ft.  i  Eq.  ft. 

per 
sq^lt. 

per 

Eq  ft. 

La 

per 
Eq.  ft. 

i 

10 

15.32 

0.13  i  0.23 

30.6 

24.5   20.4 

17.5 

15,3 

12.3 

10.2 

11 

13.93 

:  0.16  I  0.25 

25.3 

20.3   16.9 

14.5 

12.7 

10.1 

8.4 

12 

12.77 

:  0.19  i  0.27 

21.3 

17.0  !  14.2 

12.2 

10.6 

8.5 

7.1 

13 

11.78 

!  0.22  !  0.29 

18.1 

14.5    12.1 

10.4 

9.1 

1   7.2 

6.0 

14 

10.94 

1  0.26  j  0.32 

15.6 

12.5    10.4 

8.9 

7.8 

6.3 

5.2 

15 

10.21 

!0.30   0.34 

13.6 

10.9  l   9.1 

7.8 

6.8 

5.4 

4.5 

16 

9.58 

10.34   0.36 

12.0 

9.6     8.0 

6.8 

6.0 

4.8 

4.0 

17 

9.01 

0.88  0.38 

10.6 

8.5     7.1 

6.1 

5.3 

4.2 

3.5 

18 

8.51 

10.43   0.41 

9.5 

7.6     6.3 

5.4 

4.7 

3.8 

3.1 

19 

8.06 

0.48   0.43 

8.5 

6.8     5.7 

4.8 

4.2 

3.4 

2.8 

20 

7.66 

i  0.53  !  0.45 

7.7 

6.1     5.1 

4.4 

3.8 

3.1 

2.5 

21 

7.30 

iO.58   0.47 

7.0 

5.6     4.6 

4.0 

3.5 

2.8 

2.3 

22 

6.96 

10.64   0.50 

6.3 

5.1:     4.2 

3.6 

3.2 

2.5 

2.1 

23 

6.66 

I  0.70  :  0.52 

5.8 

4.6     3.9 

3.3 

2.9 

2.3 

1.9 

24 

6.38 

0.76   0.54 

5.3 

4.2     3.6 

3.0 

2.7 

2.1 

1.8 

25 

6.13 

1  0.82  i  0.56 

4.9 

3.9     3.3 

2.8 

2.5 

1.9 

1.6 

26 

5.89 

0.89   0.59 

4.5 

3.6     3.0 

2.6 

2.3 

1.8 

1.5 

27 

5.67 

0.96  ;  0.61 

4.2 

3.4     2.8 

2.4 

2.1 

1.7 

1.4 

28 

5.47 

1.03  :  0.63 

3.9 

3.1  !   2.6 

2.2 

2.0 

1.6 

1.3 

29 

5.28 

1.11   0.65 

3.6 

2.9     2.4 

2.1 

1.8 

1.5  I   1.2 

30 

5.11 

1.19  !  0.68 

3.4 

2.7     2.3 

1.9 

1.7 

1.4 

1.1 

31 

4.94 

1.27   0.70 

3.2 

2.6     2.1 

1.8 

1.6 

1.3 

1.1 

32 

4.79 

1.35  :  0.72 

3.0 

2.4     2.0 

1.7 

1.5 

1.2 

1.0 

33 

4.64 

1.44   0.74 

2.8 

2.2!   1.9 

1.6 

1.4 

1.1 

.9 

34 

4.51 

1.53  .  0.77 

2.7 

2.1     1.8 

1.5 

1.3 

1.1 

.9 

35 

4.38 

1.62   0.79 

2.5 

2.0i   1.7 

1.4 

1.3 

1.0 

.8 

36 

4.26 

1.71  ;  0.81 

2.4 

1.91    1.6 

1.4 

1.2 

.9 

.8 

37 

4.14 

1.80  i  0.83 

2.2 

1.8     1.5 

1.3 

1.1 

.9 

.7 

38 

4.03 

1.90  i  0.86 

2.1 

1.7,    1.4 

1.2 

1.1 

.8 

.7 

39 

3.93 

2.01  ;  0.88 

2.0 

1.6;  1.3 

1.2 

1.0 

.8 

.7 

1 

i 

UNION    IRON     MILLS' 

10-INCH    EYEBEAM,   No.   5,   LIGHT, 

30  LBS.  PER  FOOT. 

Depth,  10".    Width  of  Flanges,  4.32".    Thickness  of  Web,  0.32". 

Maximum  fiber  strain  =  12000  Ibs.  per  square  inch. 

II 

it*! 

-2§^§ 

i. 

b-9 

fl 

Proper  distance,  in  feet,  center  to  center 
of  beams,  for  Safe  Loads  of 

ft 

w 

i.s 

r9 

« 

100 

125 

150 

175 

200 

250 

300 

J  & 

IJfl 

i'f 

ILs 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

s  S 

sSH 

tS  M 

per 

per 

per 

per 

per 

per 

per 

=3:3.2.2 

« 

^~ 

sq.ft. 

sq.ft.    sq.ft. 

sq.ft. 

sq.ft.    sq.ft. 

sq.ft. 

10 

12.00 

0,14 

0.15 

24.0 

19.2 

16.0 

13.7 

12.0 

9.6 

8.0 

11 

10.91 

0.17 

0.17 

19.8 

15.9  !  13.2 

11.3 

9.9 

7.9 

6.6 

12 

10.00 

0.20 

0.18 

16.7 

13.3  !  11.1 

9.5 

8.3 

6.7 

5.6 

13 

9.23 

0.23 

0.20 

'14.2 

11.4 

9.5 

8.1 

7.1 

5.7 

4.7 

14 

8.57 

0.27 

0.21 

12.2 

9.8 

8.2 

7.0 

6.1 

4.9 

4.1 

15 

8.00 

0.31 

0.23 

10.7 

£.5 

7.1 

6.1 

5.3 

4.3 

3.6 

16 

7.50 

0.35 

0.24 

9.4 

7.5 

6.3 

5.4 

4.7 

3.8 

3.1 

17 

7.06 

0.40 

0.26 

8.3 

6.6 

5.5 

4.7 

4.2 

3.3 

2.8 

18 

6.67 

0.45 

0.27 

7.4 

5.9 

4.9 

4.2 

3.7 

3.0 

2.5 

19 

6.32 

0.50 

0.29 

6.7 

5.3 

4.4 

3.8 

3.3 

2.7 

2.2 

20 

6.00 

0.55 

0.30 

6.0 

4.8 

4.0 

3.4 

3.0 

2.4 

2.0 

21 

5.71 

0.61   0.32 

5.4 

4.4 

3.6 

3.1 

.2.7 

2.2 

1.8 

22 

5.45 

0.67   0.33 

5.0 

4.0 

3.3 

2.8 

2.5 

2.0 

1.7 

23 

5.22 

0.73   0.35 

4.5  !   3.6 

3.0 

2.6 

2.3 

1.8 

1.5 

24 

5.00 

0.80   0.36 

4.2     3.3 

2.8 

2.4 

2.1 

1.7 

1.4 

25 

4.80 

0.87 

0.38 

3.8     3.1 

2.6 

2.2 

1.9 

1.5 

1.3 

26 

4.62  i  0.94 

0.39 

3.6  I   2.8 

2.4 

2.0 

1.8 

1.4 

1.2 

27 

4.44    1.01    0.41 

3.3     2.6 

2.2 

1*9 

1.6 

1.3 

1.1 

28 

4.29  1  1.09   0.42 

3.1     2.4 

2.0 

1.7 

1.5 

1.2 

1.0 

29 

4.14 

1.17 

0.44 

2.9     2.3 

1.9 

1.6 

1.4 

1.1 

.9 

30 

4.00 

1.25 

0.45 

2.7     2.1 

1.8 

1.5. 

1.3 

1.1 

.9 

31 

3.87 

1.33   0.47 

2.5 

2.0 

1.7 

1.4     1.2 

1.0 

.8 

32 

3.75 

1.42  !  0.48 

2.3 

1.9 

1.6 

1.3     1.2 

.9 

.8 

33 

3.64    1.51  :  0.50 

2.2 

1.8 

1.5 

1.3     1.1       .9  i     .7 

34 

3.53    1.60  i  0.51 

2.1 

1.7 

1.4 

1.2     1.0  ;     .8 

.7 

35 

3.43    1.70  !  0.53 

2.0 

1.6     1.3 

1.1 

1.0      .8 

.7 

36 

3.33    1.80   0.54 

1.9 

1.5     1.2     1.1 

.9      .7 

.6 

37 

3.24    1.90:0.56 

1.8 

1.4     1.2 

1.0       .9 

.7 

.6 

38 

3.16    2,01  i  0.57 

1.7 

1.3     1.1 

.9       .8 

.7 

.6 

39 

3.08    2.11   0.59 

1.6  1   1.3     1.1       .9 

.8      .6 

.5 

R 

1                ' 

] 

UNION    IRON 

—  r. 
MILLS' 

10-INCH    EYEBEAM,  No. 

5,  HEAVY, 

45 

LBS.  PER  FOOT. 

Depth,  10".    Width  of  Flanges,  4.77". 

Thickness 

of  Web,  0.77". 

Maximum  fiber  strain  =  12000 

Ibs.  per  square  inch. 

I! 

1-ili 

J| 

Si 

Proper  distance, 
of  beams, 

in  feet,  center  to  center 
for  Safe  Loads  of 

1  if 

ft? 

1-9 

?5 

100       125 

150 

175 

<    200 

250 

300 

§  E, 

,~'f3 

t§  -=? 

i    5    M 

Ibs.       Ibs. 

Ibs. 

Ibs. 

!   Ibs. 

Ibs. 

Ibs. 

.2    §* 

ilLJ 

•I-2 

.|Fg 

per 

per 

per 

per 

per 

cg^.S.S 

5 

* 

cq.  ft. 

•Jft 

*fft. 

sq.  ft. 

sq.ft. 

10 

15.00 

0.14  i  0.23 

30.0  24.0 

20.0 

17.1 

!15.0 

12.0 

!10.0 

11 

13.64 

0.17  i  0.25 

24.8 

19.8 

16.5 

14.2 

!12.4 

9.9 

8.3 

12 

12.50 

0.20 

0.27 

20.8   16.7 

13.9 

11.6 

10.4 

8.3 

6.9 

13 

11.54 

0.23 

0.29 

17.8   14.2 

11.8 

10.1 

:      8.9 

7.1 

5.9 

14 

10.71 

0.27 

0.32 

15.3 

12.2 

10.2 

8.7 

:  7.7 

6.1 

5.1 

15 

10.00 

0.31 

0.34 

13.3 

10.7 

8.9 

7.6 

6.7 

5.3 

:   4.4 

16 

9.38 

0.35 

0.36 

11.7     9.4 

7.8 

6.7 

5.9 

4.7 

3.9 

17 

8.82 

0.40 

0.38 

10.4     8.3 

6.9 

5.9 

i   5.2 

4  2 

3.5 

18 

8.33 

0.45 

0.41 

9.3     7.4 

6.2 

5.3 

:   4.6 

3.7 

3.1 

19 

7.89 

0.50 

0.43 

8.3:   6.6 

5.5 

4.7 

i  4.2     3.3     2.8 

20 

7.50 

0.55 

0.45 

7.5 

6.0 

5.0 

4.3 

1   3.8 

3.0 

2.5 

21 

7.14 

0.61 

0.47 

6.8 

5.4 

4.5 

3.9 

3.4 

2.7 

2.3 

22 

6.82 

0.67 

0.50 

6.2     5.0 

4.1 

3.5 

i   3.1 

2.5 

2.1 

23 

6.52 

0.73 

0.52 

5.7     4.5 

3.8 

3.2 

2.8 

2.3 

1.9 

24 

6.25 

0.80 

0.54 

5.2     4.1 

3.5:   2.9 

2.6 

2.1 

1.7 

25 

6.00 

0.87 

0.56 

4.8 

3.8 

3.2 

2.7 

2.4     1.9 

1.6 

26 

5.77 

0.94 

0.59 

4.4     3.6 

3.0 

2.5 

2.2!    1.8 

1.5 

27 

5.56 

1.01 

0.61 

4.1  i   3.3 

2.8 

2.4 

2.1 

1.6 

1.4 

28 

5.36 

1.09 

0.63 

3.8     3.1 

2.6 

2.2 

1.9 

1.5 

1.3 

29 

5.17 

1.17 

0.65 

3.6     2.9 

2.4 

2.0 

1.8 

1.4 

1.2 

30 

5.00 

1.25 

0.68 

3.3     2.7 

2.2 

1.9 

1.7 

1.3 

1.1 

31 

4.84 

1.33 

0.70 

3.1     2.5 

2.1 

1.8 

1.6 

1.2 

1.0 

32 

4.69 

1.42 

0.72 

2.9     2.3 

1.9 

1.7 

1.5 

1.2 

1.0 

33 

4.55 

1.51 

0.74 

2.8!  2.2 

1.8 

1.6 

1.4 

1.1 

.9 

34 

4.41 

1.60 

0.77 

2.6 

2.1 

1.7 

1.5 

1.3 

1.0 

.9 

35 

4.29 

1.70 

0.79 

2.4 

2.0 

1.6 

1.4 

1.2 

1.0 

.8 

36 

4.17 

1.80 

0.81 

2.3 

1.9 

1.5 

1.3 

1.2 

.9 

.8 

37 

4.05 

1.90 

0.83 

2.2 

1.8 

1.5 

1.3 

1.1 

.9 

.7 

38 

3.95 

2.01 

0.86 

2.1 

1.7 

1.4 

1.2 

1.0 

.8 

.7 

39 

3.85 

2.11 

0.88 

2.0 

1.6 

1.3 

1.1 

1.0 

.8 

.7 

SB 

UNION     IRON     MILLS' 

9-INCH    EYEBEAM,   No.    6,    LIGHT, 

23^ 

LBS.  PER  FOOT. 

Depth,  9".    Width  of  Flanges,  4.01".    Thickness  of  Web,  0.26". 

Maximum 

fiber 

strain  =  12000  Ibs.  per  square  inch. 

a  H-s 

•£^?^ 

.2 

"3    eft 

.* 

Proper  distance,  in  feet,  center  to  center 

II 

JlMs 

bl 

f 

of  beams,  for  Safe  Loads  of 

if 

35*5 

la 

5i 

100 

125 

150       175 

200 

250      800 

.2  a 

j=.o'|  g 

iif 

fls 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs.    |    Ibs. 

s  S 

ll.s.s 

Ji  Jj 

|f 

per 

sq.  ft. 

per 
sq.ft. 

per 
sq.ft. 

per 
sq.ft. 

per 
sj.ft. 

per    !   per 

sq.  ft.  j  sq.  ft. 

10 

8.68 

0.15 

0.12 

17.4 

13.9   11.6 

9.9  i   8.7 

6.9!    5.8 

11 

7.89 

0.19 

0.13 

14.4 

11.51   9.6 

8.2|   7.2!   5.7     4.8 

12 

7.23 

0.22 

0.14 

12.1 

9.6 

8.0     6.9     6.0     4.8     4.0 

13 

6.68 

0.26 

0.15 

10.3 

8.2 

6.9     5.9!   5.1     4.1     3.4 

14 

6.20 

0.30 

0.16 

8.9 

7.1 

5.9,  5.1     4.4 

3.5  |    2.9 

15 

5.79 

0.35 

0.18 

7.7 

6.2 

5.1     4.4     3.9     3.1  1    2.6 

16 

5.43 

0.40 

0.19 

6.8 

5.4     4.5     3.9     3.4     2.7     2.3 

17 

5.11 

0.45 

0.20 

6.0 

4.8     4.0     3.4     3.0     2.4     2.0 

18 

4.82 

0.50 

0.21 

5.4 

4.3     3.6     3.0 

2.7    2.1 

1.8 

19 

4.57 

0.56 

0.22 

4.8 

3.8     3.2     2.7 

2.4     1.9     1.6 

20 

4.34 

0.62 

0.24 

4.3 

3.5 

2.9 

2.5 

2.2     1.7 

1.4 

21 

4.13 

0.68 

0.25 

3.9 

3.2 

2.6     2.2     2.0     1.6 

1.3 

22 

3.95 

0.75 

0.26 

3.6 

2.9 

2.4     2.0     1.8,    1.4 

1.2 

23 

3.77 

0.82 

0.27 

3.3 

2.6 

2.2  i   1.9     1.6     1.3 

1.1 

24 

3.62 

0.89 

0.28 

3.0 

2.4 

2.0 

1.7 

1.5 

1.2 

1.0 

25 

3.47 

0.96 

0.29 

2.8 

2.2 

1.9 

1.6 

1.4 

1.1 

.9 

26 

3.34 

1.04 

0.31 

2.6 

2.0 

1.7 

1.5 

1.3 

1.0  i     .9 

27 

3.21 

1.12 

0.32 

2.4 

1.9     1.6 

1.4 

1.2 

1.0 

.8 

28 

3.10 

1.20 

0.33 

2.2 

1.8 

1.5     1.3 

1.1 

.9 

.7 

29 

2.99 

1.29 

0.34 

2.1 

1.6 

1.4 

1.2 

1.0 

.8 

.7 

30 

2.89 

1.39 

0.35 

1.9 

1.5     1.3 

1.1 

1.0 

.8 

.6 

31 

2.80 

1.48 

0.36 

1.8 

1.4     1.2 

1.0 

.9      .7 

.6 

32 

2.71 

1.58 

0.38 

1.7 

1.4     1.1 

1.0 

.9      .7 

.6 

33 

2.63 

1.68 

0.39 

1.6 

1.3  i   1.1 

.9 

.8 

.6 

.5 

34 

2.55 

1.78 

0.40 

1.5 

1.2     1.0 

.9 

.8      .6 

.5 

35 

2.48 

1.89 

0.41 

1.4 

1.1       .9 

.8 

.7 

.6 

.5 

36 

2.41 

2.00 

0.42 

1.3 

1.1 

Q 

.y 

.8 

.7 

.5 

.4 

37 

2.35 

2.11 

0.43 

1.3 

1.0 

.8 

.7      .6 

.5 

.4 

38 

2.28 

2.22 

0.45 

1.2 

1.0 

.8      .7      .6 

.5 

.4 

39 

2.23 

2.34 

0.46 

1.2 

.9 

.8      .7      .6 

.5 

.4 

x?  — 

, 

—  ^ 

UNION     IRON     MILLS' 

9-INCH    EYEBEAM,   No.    6,    HEAVY, 

33 

LBS.  PER  FOOT. 

Depth,  9".    Width  of  Flanges,  4.33". 

Thickness  of  Web,  0.58". 

Maximum  fiber 

strain  =  12000  1 

bs.  per  square  inch. 

rt   -*s 

tif^l-i- 

.3 
-J§ 

Proper  distance, 

in  feet,  center  to  center 

11 

|§j§ 

K.2 

a^ 

of  b 

earns, 

for  Safe  Loads  of 

j.a 

i'^s 

f.a 

Ja  t=~> 

g  -2" 

^3  "^  CM 
ng-S-gjO 

c4 

§"" 

*°  <*-! 

ICO 

125 

150 

175 

200 

250       300 

il  ^* 

J;g'|    | 

••g-^" 

2a  w 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

3  f 

-*5    w    feJD^* 

JJ 

•sj 

per 

per 

per 

per 

per 

per 

per 

& 

£= 

Eq.  ft. 

sq.ft. 

sq.  ft. 

sq.  ft. 

sq.ft. 

sq.  ft.    sq.  ft 

10 

10.40 

0.15 

0.17 

20.8   16.6 

13.9 

11.9 

10.4     8.3'   6.9 

11 

9.45 

0.19 

0.18 

17.2   13.8 

11.5 

9.8 

8.6 

6.9:   5.7 

12 

8.67 

0.22 

0.20 

14.5    11.6 

9.6 

8.3 

7.2     5.8  I   4.8 

13 

8.00 

0.26 

0.22 

12.3     9.8 

8.2 

7.0 

6.2     4.9     4.1 

14 

7.43 

0.30 

0.23 

10.6     8.5 

7.1 

6.1 

5.3     4.2 

3.5 

15 

6.93 

0.35 

0.25 

9.2     7.4 

6.2 

5.3 

4.6     3.7 

3.1 

16 

6.50 

0.40 

0.26 

8.1     6.5 

5.4 

4.6 

4.1     3.3     2.7 

17 

6.12 

0.45 

0.28 

7.2 

5.8 

4.8 

4.1 

3.6     2.9     2.4 

18 

5.78    0.50 

0.30 

6.4 

5.1 

4.3 

3.7 

3.2 

2.6     2.1 

19 

5.47 

0.56 

0.31 

5.8 

4.6 

3.8 

3.3 

'2.9     2.3 

1.9 

20 

5.20    0.62 

0.33 

5.2 

4.2 

3.5 

3.0 

2.6     2.1 

1.7 

21 

4.95  !  0.68 

0.35 

4.7!   3.8 

3.1 

2.7 

2.4 

1.9 

1.6 

22 

4.73    0.75 

0.36 

4.3     3.4 

2.9 

2.5 

2.2     1.7 

1.4 

23 

4.52 

0.82 

0.38 

3.9     3.1 

2.6 

2.3 

2.0 

1.6 

1.3 

24 

4.33 

0.89 

0.40 

3.6     2.9 

2.4 

2.1 

1.8 

1.4 

1.2 

25 

4.16 

0.96' 

0.41 

3.3     2.7 

2.2 

1.9 

1.7 

1.3 

1.1 

26 

4.00 

1.04 

0.43 

3.1     2.5 

2.1 

1.8 

1.5 

1.2 

1.0 

27 

3.85 

1.12 

0.45 

2.9     2.3 

1.9 

1.6 

1.4 

1.1 

.9 

28 

3.71 

1.20 

0.46 

2.7i   2.1 

1.8 

1.5 

1.3 

1.1       .9 

29 

3.59 

1.29 

0.48 

2.5 

2.0 

1.6 

1.4 

1.2 

1.0  1     .8 

30  v 

3.47 

1.39 

0.50 

2.3     1.8 

1.5 

1.3 

1.2       .9      .8 

31 

3.35 

1.48 

0.51 

2.2     1.7 

1.4 

1  2 

1.1       .9 

.7 

32 

3.25  !  1.58 

0.53 

2.0 

1.6 

1.4 

1.1 

1.0      .8       .7 

33 

3.15  :  1.68 

0.55 

1.9 

1.5 

1.3 

1.1 

1.0      .8       .6 

34 

3.06    1.78 

0.56 

1.8 

1.4 

1.2 

1.0 

.9      .7      .6 

35 

2.97 

1.89 

0.58 

1.7 

1.4 

1.1 

1.0 

.9       .7      .6 

36 

2.89    2.00 

i  0.59 

1.6 

1.3 

1.1 

.9 

.8 

.6      .5 

37 

2.81    2.11 

0.61 

1.5 

1.2 

1.0 

.9 

.8 

.6 

t 

38 

2.74    2.22 

0.63 

1.4 

1.21   1.0 

.8 

.7 

.6 

£ 

39 

2.67 

2.34 

0.64 

1.4     U 

.9 

.8 

.7      .5 

.5 

UNION    IRON    MILLS' 

8-INCH    EYEBEAM,   No.    8,   LIGHT, 

22   LBS.  PER  FOOT. 

Depth,  8".    Width  of  Flanges,  3.81  ".    Thickness  of  Web,  0.31  ". 

Maximum  fiber  strain  =  12000  Ibs.  per  square  inch. 

|rf     -,: 

Proper  distance,  in  feet,  center  to  center 

I  * 

ills 

il 

•2  .3 

|s 

of  beams,  for  Safe  Loads  of 

tS  ~ 

5]f:3«g 

2  -a 

""•M 

ICO 

125 

150       175 

200 

250 

300 

0  j?'S    f. 

•-§  ij  i  ;2  ° 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

1   1* 

~Z'B  fl-2 

J>  J>   j  -|f  1 

per 

per 

per 

per    i  per 

per    j   per 

<§i.s.s 

«        |  £=~ 

sq.  ft. 

sq.ft. 

£q.  ft.    sq.  ft. 

sq.  ft. 

sq.  ft.  i  sq.  ft. 

5 

14.00 

0.04   0.06 

56.0 

44.8  1  37.3   32.0 

28.0 

22.4   18.7 

6 

11.67 

0.08  I  0.07 

38.9 

31.1   25.9 

22.2 

19.5 

15.6   13.0 

7 

10.00 

0.08  0.08 

28.6 

22.9   19.0 

16.3 

14.3 

11.4 

9.5 

8 

8.75 

0.11 

0.09 

21.9 

17.5   14.6 

12.5 

10.9 

8.8 

7.3 

9 

7.78 

0.14 

0.10 

17.3 

13.8 

11.5 

9.9 

8.6 

6.9 

5.8 

10 

7.00 

0.17 

0.11 

14.0 

11.2 

9.3 

8.0 

7.0 

5.6 

4.7 

11 

6.36 

0.21  i  0.12 

11.6 

9.2 

7.7 

6.6 

5.8 

4.6 

3.9 

12 

5.83 

0.25   0.13 

9.7 

7.8 

6.5 

5.8 

4.9 

3.9 

3.2 

13 

5.38 

0.29  0.14 

8.3 

6.6 

5.5 

4.7 

4.1 

3.3 

2.8 

14 

5.00 

0.34 

0.15 

7.1 

5.7 

4.8 

4.1 

3.6 

2.9 

2.4 

15 

4.67 

0.39 

0.17 

6.2 

5.0 

4.2 

3.6 

3.1 

2.5 

2.1 

16 

4.38 

0.44 

0.18 

5.5 

4.4 

3.7 

3.1 

2.7 

2.2 

1.8 

17 

4.12 

0.50 

0.19 

4.9 

3.9 

3.2 

2.8     2.4 

1.9     1.6 

18 

3.89 

0.56 

0.20 

4.3 

3.5 

2.9 

2.51   2.2 

1.7     1.4 

19 

3.68 

0.62 

0.21 

3.9 

3.1 

2.6 

2.2 

1.9 

1.5 

1.3 

20 

3.50 

0.69 

0.22 

3.5 

2.8 

2.3 

2.0 

1.8 

1.4 

1.2 

21 

3.33 

0.76 

0.23 

3.2 

2.5 

2.1 

1.8 

1.6 

1.3 

1.1 

22 

3.18 

0.84 

0.24 

2.9 

2.3 

1.9 

1.7 

1.4 

1.2 

1.0 

23 

3.04  1  0.92 

0.25 

2.6 

2.1 

1.8 

1.5 

1.3 

1.1 

.9 

24 

2.92    1.00 

0.26 

2.4 

1.9 

1.6 

1.4 

1.2 

1.0 

.8 

25 

2.80    1.08 

0.28 

2.2 

1.8 

1.5 

1.3 

1.1 

Q 

.7 

26 

2.69    1.17 

0.29 

2.1 

1.7* 

1.4 

1.2 

1.0 

8 

.7 

27 

2.59  !  1.26 

0.30 

1.9 

1.5 

1.3 

1.1 

i.b 

!s 

.6 

28 

2.50  i  1.36   0.31 

1.8 

1.4 

1.2 

1.0 

.9 

.7 

.6 

29 

2.41     1.46 

0.32 

1.7 

1.8 

1.1 

.9 

.8 

.7 

.6 

30 

2.33 

1.56 

0.33 

1.6 

1.2 

1.0 

.9 

.8 

.6 

.5 

31 

2.26 

1.67 

0.34 

1.5 

1.2 

1.0 

.8 

.7 

.6 

.5 

32 

2.19 

1.78 

0.35 

1.4 

1.1 

.9 

.8 

.7 

.5 

.5 

33 

2.12 

1.89 

0.36 

1.3 

1.0 

.9 

.7 

.6 

.5 

.4 

34 

2.06 

2.00 

0.37 

1.2 

1.0 

.8 

.7 

.6 

.5 

.4 

4  

! 

i 

UNION    IRON    MILLS' 

8-INCH    EYEBEAM,   No.    8,    HEAVY, 

35  LBS.  PER  FOOT. 

Depth,  8".    Width  of  Flanges,  4.29".    Thickness  of  Web,  0.79". 

Maximum  fiber  strain  =  12000  Ibs.  per  square  inch. 

g  -g 

fA?J*|j 

.a  . 

Proper  distance,  in  feet,  center  to  center 

II 

111  1  j| 

jj 

of  beams,  for  Safe  Loads  of 

11 

3^2     *rt 

100 

125 

150 

175 

200 

250       300 

1  1 

,2^'S  ft    £•& 

3     M 

Ibs. 

Ibs.      Ibs. 

Ibs. 

Ibs.      Ibs.      Ibs. 

-*°  ^    S    ^   <    C3  ^ 

"fi  o 

per 

per       per 

per 

per       per 

psr 

l^.a.a 

a 

^ 

sq.ft. 

sq.  ft.    £q.  ft.    sq.  ft.    sq.  ft.    sq.  ft. 

sq.  ft. 

5 

18.08 

0.04   0.09 

72.3  57.9   48.2   41.3   36.2   28.9 

24.1 

6 

15.07 

0.06 

0.11 

50.2  40.2   83.5  28.7  125.1  1  20.1 

16.7 

7 

12.91 

0.08 

0.12 

36.9  129.5   24.6   21.1 

18.4    14.8 

12.3 

8 

11.30 

0.11 

0.14 

28.3122.6   18.8   16.1 

14.1  ;  11.3     9.4 

9 

10.04 

0.14 

0.16 

22.3  :  17.8    14.9 

12.7 

11.2     8.9 

7.4 

10 

9.04    0.17 

0.18 

18.1 

14.5   12.1    10.3 

9.0     7.2 

6.0 

11 

8.22 

0.21 

0.19 

14.9 

12.0 

10.0     8.5     7.5  '   6.0 

5.0 

12 

7.53 

0.25 

0.21 

12.6 

10.0 

8.4     7.2     6.3     5.0 

4.2 

13 

6.95 

0.29 

0.23 

10.7 

8.6     7.1     6.1 

5.3     4.3 

3.6 

14 

6.46 

0.34 

0.25 

9.2 

7.4 

6.2 

5.3 

4.6     3.7 

3.1 

15 

6.03 

0.39 

0.26 

8.0 

6.4     5.4 

4.6 

4.o!   3.2 

2.7 

16 

5.65 

0.44 

0.28 

7.1 

5.6 

4.7 

4.0 

3.5     2.8 

2.4 

17 

'  5.32 

0.50 

0.30 

6.3 

5.0     4.2 

3.6     3.1     2.5 

2.1 

18 

5.02 

0.56 

0.32 

5.6 

4.5 

3.7 

3.2     2.8 

2.2 

1.9 

19 

4.76 

0.62 

0.33 

5.0 

4.0 

3.3 

2.9 

2.5 

2.0 

1.7 

20 

4.52 

0.69 

0.35 

4.5 

3.6     3.0 

2.6 

2.3 

1.8 

1.5 

21 

4.30 

0.76 

0.37 

4.1 

3.3     2.7 

2.3 

2.0 

1.6 

1.4 

22 

4.11 

0.84 

0.39 

3.7 

3.0     2.5 

2.1 

1.9     1.5 

1.2 

23 

3.93 

0.92   0.40 

3.4 

2.7     2.3 

2.0 

1.7 

1.4 

1.1 

24 

3.77 

1.00 

0.42 

3.1 

2.5     2.1 

1.8 

1.6 

1.3 

1.0 

25 

3.62 

1.08 

0.44 

2.9 

2.3 

1.9 

1.7 

1.4 

1.2 

1.0 

26 

3.48 

1.17 

0.46 

2.7 

2.1 

1.8 

1.5 

1.3 

1.1 

.9 

27 

3.35 

1.26 

0.47 

2.5 

2.0 

1.6 

1.4 

1.2 

1.0 

.8 

28 

3.23 

1.36 

0.49 

2.3 

1.8 

1.5 

1.3 

1.2 

.9 

.8 

29 

3.12     1.48 

0.51 

2.2 

1.7 

1.4 

1.2 

1.1 

.9 

.7 

30 

3.01 

1.56 

0.53 

2.0 

1.6 

1.3 

1.1 

1.0 

.8 

.7 

31 

2.92 

1.67 

0.54 

1.9 

1.5 

1.2 

1.1 

.9 

.8 

.6 

32 

2.83 

1.78 

0.56 

1.8 

1.4 

1.2 

1.0 

.9 

.7 

.6 

33 

2.74 

1.89  1  0.58 

1.7 

1.3 

1.1 

.9 

.8 

.7 

.6 

34 

2.66 

2.00   0.60 

1.6     1.2 

1.0 

.9 

.8 

.6 

.5 

46 

UNION    IRON    MILLS' 

7-INCH   EYEBEAM,   No.   9,   LIGHT, 

18  LBS.  PER  FOOT. 

Depth,  1".    Width  of  Flanges,  3.61".    Thickness  of  Web,  0.23". 

Maximum  fiber  strain  =  12000  Ibs.  per  square  inch. 

g 

l^^j  .1^   .SM. 

Proper  distance,  in  feet,  center  to  center 

1  * 

iici  •la 

J§ 

of  beams,  for  Safe  Loads  of 

1  "^ 

0   ^  °  ^  i  S  "~* 

•8* 

100      125 

150       175 

200       250 

300 

1  1 

j=jTg    g        -^^-         ^     M 

Ibs.      Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

=2  -S  t,^    <S  -3      '3  <= 

per    1  per 

per 

per 

per 

per 

per 

JB^.S.2   £        £=~ 

sq.  ft.    sq.  ft. 

sq.ft.    sq.ft. 

sq.  ft. 

sq.ft. 

sq.  ft. 

5 

10.48    0.05  ''0.05 

41.9   33.5  27.9 

24.0 

21.0 

16.8 

14.0 

6 

8.73 

0.07  0.05 

29.1   23.3  19.4 

16.6 

14.6 

11.6 

9.7 

7 

7.49 

0.10  0.06 

21.4 

17.1   14.3 

12.2 

10.7 

8.6 

7.1 

8 

6.55    0.13  0.07 

16.4 

13.1   10.9 

9.4 

8.2 

6.6 

5.5 

9 

5.82  |  0.16 

0.08 

12.9 

10.3     8.6     7.4 

6.5 

5.2 

4.3 

10 

5.24    0.20 

0.09 

10.5 

8.4 

7.0 

6.0 

5.2 

4.2 

3.5 

11 

4.76 

0.24 

0.10 

8.7 

6.9 

5.8 

4.9 

4.3 

3.5 

2.9 

12 

4.37 

0.28 

0.11 

7.3 

5.8 

4.9 

4.2 

3.6 

2.9 

2.4 

13 

4.03 

0.33 

0.12 

6.2 

5.0 

4.1 

8.5 

3.1 

2.5 

2.1 

14 

3.74 

0.39 

0.13 

5.3 

4.3 

3.6 

3.1 

2.7 

2.1 

1.8 

15 

3.49 

0.45 

0.14 

4.7 

3.7 

3.1     2.7 

2.3 

1.9 

1.6 

16 

3.28 

0.51 

0.14 

4.1  i   3.3 

8.7    2.3 

2.1 

1.6 

1.4 

17 

3.08 

0.57 

0.15 

3.6 

2.9 

2.4 

2.1 

1.8 

1.4 

1.2 

18 

2.91 

0.64 

0.16 

3.2 

2.6 

2.2 

1.8 

1.6 

1.3 

1.1 

19 

2.76 

0.71 

0.17 

2.9 

2.3 

1.9 

1.7 

1.5 

1.1 

1.0 

20 

2.62 

0.79 

0.18 

2.6 

2.1 

1.7 

1.5 

1.3 

1.0 

.9 

21 

250 

0.87 

0.19 

2.4 

1.9 

1.6 

1.4 

1.2 

1.0 

.8 

22 

2.38 

0.96 

0.20 

2.2 

1.7 

1.4 

1.2 

1.1 

.9 

.7 

23 

2.28 

1.05 

0.21 

2.0 

1.6 

1.3 

1.1 

1.0 

.8 

.7 

24 

2.18 

1.14 

0.22 

1.8 

1.4 

1.2 

1.0 

.9 

.7 

.6 

25 

2.10 

1.24 

0.23 

1.7 

1.3 

1.1 

1.0 

.8 

.7 

.6 

26 

2.02 

1.34 

0.23 

1.6 

1.2 

1.0 

.9 

.8 

.6 

.5 

27 

1.94 

1.44 

0.24 

1.4 

1.2 

1.0 

.8 

.7 

.6 

.5 

28 

1.87 

1.55 

0.25 

1.3 

1.1 

.9 

.8 

.7 

.5 

.4 

29 

1.81 

1.66 

0.26 

1.2 

1.0 

.8 

.7 

.6 

.5 

.4 

47 


TV                                                                                                                                                                                       CT 

UNION    IRON 

MILLS' 

7-INCH    EYEBEAM,   No.    8,   HEAVY, 

25  LBS.  PER  FOOT. 

Depth,  1".    Width  of  Flanges,  3.91". 

Thickness  of  Web,  0.53". 

Maximum  fiber  strain  =  12000 

Ibs.  per  square  inch. 

«  ^ 

ti^s"  1  • 

.3  M. 

Proper  dis 

tance,  in  feet,  center  to  center 

Jpi 

|I||  l| 

Jfj 

oft 

earns,  for  Safe  Loads  of 

•^ 

vrfS*-    ^'2 

100       125 

150 

175 

200 

250 

300 

.§  §< 

3|f| 

•£"3       S   m 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

«  « 

Jj.2 

•3$ 

per 

per 

per 

per 

per 

per 

per 

l^.a.2 

A 

& 

sq.ft. 

sq.  ft. 

sq.ft.     sq.ft.    sq.ft.    sq.ft. 

sq.  ft. 

. 

5 

12.40 

0.05   0.06 

49.6   39.7 

33.1    28.3   24.8    19.8 

16.5 

6 

10.33 

0.07   0.08 

34.4 

27.5 

123.0    19.7    17.2    13.8 

11.5 

7 

8.86 

0.10 

0.09 

25.3 

20.2 

;16.9    14.5    12.7    10.1     8.4 

8 

7.75 

0.13 

0.10 

19.4 

15.5 

12.9 

11.1     9.7,   7.8     6.5 

9 

6.89 

0.16 

0.11 

15.3 

12.2 

10.2     8.7 

7.71   6.1 

5.1 

10 

6.20 

0.20   0.13 

12.4     9.9 

8.3  '   7.1     6.2     5.0     4.1 

11 

5.64 

0.24 

0.14 

10.3     8.2 

6.8     5.9     5.1     4.1     3.4 

12 

5.17    0.28 

0.15 

8.6     6.9 

5.7     4.9     4.3     3.4     2.9 

13 

4.77 

0.33   0.16 

7.3     5.9 

4.9     4.2     3.7     2.9     2.4 

14 

4.43 

0.39   0.18 

6.3     5.1 

4.2     3.6     3.2     2.5     2.1 

15 

4.13 

0.45 

0.19 

5.5     4.4 

3.7!   3.1     2.8     2.2 

1.8 

16 

3.88 

0.51 

0.20 

4.9     3.9 

3.2     2.8 

2.4 

1.9 

1.6 

17 

3.65 

0.57 

0.21 

4.3     3.4 

2.9     2.5 

2.1 

1.7 

1.4 

18 

3.44 

0.64 

0.23 

3.8 

3.1 

2.5     2.2 

1.9 

1.5 

1.3 

19 

3.26 

0.71 

0.24 

3.4 

2.7 

2.3  !   2.0 

1.7 

1.4 

1.1 

20 

3.10 

0.79 

0.25 

3.1 

2.5 

2.1 

1.8 

1.5 

1.2 

1.0 

21 

2.95 

0.87  .  0.26 

2.8     2.2 

1.9 

1.6 

1.4 

1.1 

.9 

22 

2.82 

0.96 

0.28 

2.6 

2.0 

1.7 

1.5 

1.3 

1.0 

.9 

23 

2.70 

1.05 

0.29 

2.4 

1.9 

1.6 

1.3 

1.2 

.9 

.8 

24 

2.58 

1.14 

0.30 

2.2 

1.7,   1.4 

1.2 

1.1       .9 

.7 

25 

2.48 

1.24   0.31 

2.0 

1.6 

1.3 

1.1 

1.0      .8 

.7 

26 

2.38 

1.34   0.33 

1.8 

1.5 

1.2 

1.0 

.9 

.7 

.6 

27 

2.30 

1.44 

0.34 

1.7 

1.4 

1.1 

1.0 

.9 

.7 

.6 

28 

2.21 

1.55 

0.35 

1.6 

1.3 

1.1 

.9 

.8 

.6      .5 

29 

2.14 

1.66 

0.36 

1.5 

1.2 

1.0 

.8 

.7 

.6 

.5 

£ 

48 

-.A: 

5  — 

• 

UNION     IRON 

MILLS' 

6-INCH    EYEBEAM,   No.    10,   LIGHT, 

13^   LBS.  PEE, 

FOOT. 

Depth,  6".     Width  of  Flanges,  3.24". 

Thickness  of  "Web,  0.24". 

Maximum  fiber  strain  =  12000 

Ibs.  per  square  inch. 

|| 

ill 

Si 

|| 

Proper  distance, 
of  beams, 

in  feet,  center  to  center 
for  Safe  Loads  of 

i  -J 

•li^c 

|s 

O  ^ 

100 

125 

150 

175 

200 

250 

300 

1  1 

gj-s'g 

•_£3  T3 

-t-3        O 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

llfj 

j- 

fl 

per 

sq,  ft. 

per 

sq.ft. 

per 
sq.ft. 

per 

per 

sq.  ft. 

per 

sq.  ft. 

per 
sq.ft. 

5 

6.53 

0.06 

0.03 

26.1 

20.9 

17.4 

14.9 

13.1 

10.4 

8.7 

6 

5.44     0.08 

0.04 

18.1 

14.5 

12.1 

10.4 

9.1 

7.3 

6.0 

7 

4.66     0.11 

0.05 

13.3 

10.6 

8.9 

7.6 

6.7 

5.3 

4.4 

8 

4.08     0.15 

0.05 

10.2 

8.2 

6.8 

5.8 

5.1 

4.1 

3.4 

9 

3.63     0.19 

0.06 

8.1 

6.5 

5.4 

4.6 

4.0 

3.2 

2.7- 

10 

3.26     0,23 

0.07 

6.5. 

5.2 

4.4 

3.7 

3.3 

2.6 

2.2 

11 

2.97     0.28 

0.07 

5.4 

4.3 

3.6 

3.1 

2.7 

2.2 

1.8 

12 

2.72 

0.33 

0.08 

4.5 

3.6 

3.0 

2.6 

2.3 

1.8 

1.5 

13 

2.51 

0.39 

0.09 

39 

3.1 

2.6 

2.2 

1.9 

1.5 

1.3 

14 

2.33 

0.45 

0.09 

3^3 

2.7 

2.2 

1.9 

1.7 

1.3 

1.1 

15 

2.18 

0.52 

0.10 

2.9 

2.3 

1.9 

1.7 

1.5 

1.2  \   1.0 

16 

2.04 

0.59 

0.11 

2.6 

2.0 

1.7 

1.5 

1.3 

1.0       .9 

17 

1.92 

0.67 

0.11 

2.3 

1.8 

1.5 

1.3 

1.1 

.9       .8 

18 

1.81 

0.75 

0.12 

2.0 

1.6 

1.3 

1.11   1.0 

.8       .7 

19 

1.72 

0.83 

0.13 

1.8 

1.4 

1.2 

1.0  !     .9       .7 

.6 

| 

20 

1.63 

0.92 

0.14 

1.6 

1.3 

1.1 

.9  !     .8       .7 

.5 

21 

1.55     1.01 

0.14 

1.5 

1.2 

1.0 

.8       .7  !     .6 

.5 

22 

1.48     1.11 

0.15 

1.8 

1.1 

.9 

.8       .7       .5 

\5 

23 

1.42     1.22 

0.16 

1.2 

1.0 

.8 

.7      .6  '     .5 

]4 

24 

1.36     1.33 

0.16 

1.1 

.9 

.7 

.6  j     .6       .5 

.4 

25 

1.31    ,  1.45 

0.17 

1.0 

.8 

.7 

.6 

.5 

.4 

.4 

26 

1.26    11.56 

0.18 

1.0 

.8 

.6 

.5 

.5 

.4 

.3 

27 

1.21    il.68 

0.18 

.9 

.7 

.6 

.5 

.4 

.4 

.3 

28 

1.17     1.81 

0.19 

.8 

.7 

.0 

.5 

.4 

.3 

.3 

29 

1.13     1.95 

0.20 

.8 

.6 

.5 

•4 

.4 

.3 

.3 

£K 

UNION     IRON     MILLS' 

6-INCH    EYEBEAM,   No.    10,   HEAVY, 

18 

LBS.  PER  FOOT. 

Depth,  6".    Width  of  Flanges,  3.46".    Thickness  of  Web,  0.46". 

Maximum  fiber 

strain  =  12000  Ibs.  per  square  inch. 

g    *5 

ti^s 

a* 

JS  ' 

Proper  distance, 

in  feet,  center  to  center 

1  «! 

o'g  Jjo 

•ll 

J^^ 

of  beams, 

for  Safe  Loads  of 

"S  .s 

3  '*~f*4-1  <==> 

8 

If 

-3-^4? 

ijjj 

®  5 

100 

125 

150 

175 

200 

250 

300 

_i  §. 

'•§•5 

3  s 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

•M  e 

<*H    W    00 

«§  .2 

'S  5 

per 

per 

per 

per 

per 

per  ' 

per   . 

wS^S.2.2 

« 

^ 

sq.  ft. 

sq.  ft. 

sq.  ft. 

sq.  ft. 

sq.ft. 

sq.ft. 

sq.  ft. 

5 

7.58 

0.06 

0.05 

30.3 

24.3 

20.2 

17.3 

15.2 

12.1 

10.1 

6 

6.32 

0.08 

0.05 

21.1 

16.9 

14.0 

12.0 

105 

8.4 

7.0 

7 

5.42 

0.11 

0.06 

15.5 

12.4 

10.3 

8.9 

7.7 

6.2 

5.2 

8 

4.74 

0.15 

0.07 

11.9 

9.5 

7.9 

6.8 

5.9 

4.7 

4.0 

9 

4.21 

0.19 

0.08 

9.4 

7.5 

6.2 

5.3 

4.7 

3.7 

3.1 

10 

3.79 

0.23 

0.09 

7.6 

6.1 

5.1 

4.3 

3.8 

3.0 

2.5 

11 

3.45 

0.28 

0.10 

6.3 

5.0 

4.2 

3.6 

3.1 

2.5 

2.1 

12 

3.16 

0.33 

0.11 

5.3 

4.2 

3.5 

3.0     2.6     2.1 

1.8 

13 

2.92 

0.39 

0.12 

4.5 

3.6 

3.0 

2.6 

2.2 

1.8 

1.5 

14 

2.71 

0.45 

0.13 

3.9 

3.1 

2.6 

2.2 

1.9 

1.5 

1.3 

15 

2.53 

0.52 

0.14 

3.4 

2.7 

2.2 

1.9 

1.7 

1.3 

1.1 

16     . 

2.37 

0.59 

0.14 

3.0 

2.4 

2.0 

1.7 

1.5 

1.2 

1.0 

17 

2.23 

0.67 

0.15 

2.6 

2.1     1.7 

1.5 

1.3 

1.0 

.9 

18 

2.11 

0.75 

0.16 

2.3 

1.9     1.6 

1.3 

1.2 

.9 

.8 

19 

2.00 

0.83 

0.17 

2.1 

1.7     1.4 

1.2 

1.1 

.8 

.7 

20 

1.90     0.92 

0.18 

1.9 

1.5     1.3 

1.1 

1.0 

.8 

.6 

21 

1.81 

1.01  |  0.19 

1.7 

1.4     1.1 

1.0 

.9 

.7 

.6 

22 

1.72 

1.11 

0.20 

1.6 

1.2 

1.0 

.9 

.8 

.6 

.5 

23 

1.65 

1.22 

0.21 

1.4 

1.1 

1.0 

.8 

.7 

.6 

.5 

24 

1.58 

1.33 

0.22 

1.3 

1.1 

.9 

.8 

.7 

.5 

.4 

25 

1.52 

1.45 

0.23 

1.2 

1.0 

.8 

.7 

.6 

.5 

.4 

26 

1.46 

1.56 

0.23 

1.1 

.9      .7 

.6 

.6 

.4 

.4 

27 

1.40 

1.68 

0.24 

1.0 

.81     .7  . 

.6 

.5 

.4 

.3 

28 

1.35 

1.81 

0.25 

1.0 

.8       .6 

.5 

.5 

.4 

.3 

29 

1.31 

1.95; 

0.26 

.9- 

.7      .6 

.5 

.5 

.4 

.3 

1 

y> 

UNION     IRON     MILLS' 

—  r. 

5-INCH 

EYEBEAM,   No.    11,   LIGHT, 

10 

LBS.  PER  FOOT. 

Depth,  5".    Width  of 

Flanges,  2.73".    Thickness  of  Web 

,  0.225". 

Maximum  fiber 

strain  =  12000  Ibs.  per  square  inch. 

Distance  between 
supports,  in  feet. 

Safe  load,  uniformlv 
distributed,  (includ- 
ing weight  of  beam,) 
in  tons  of  2000  Ibs. 

F>  i  Daflection  under  this 
^  load,  in  inches. 

a 

a 

j§ 
••s~ 

-*.»  ° 

§i 
|i 

0.03 

Proper  distance,  in  feet,  center  to  center 
of  beams,  for  Safe  Loads  of 

100 
Ibs. 
per 

sq.  ft. 

15.8 

125 
Ibs. 
per 

•Eft. 

12.6 

150 

Ibs. 

& 

175 
Ibs. 
per 
sq.  ft. 

200 
Ibs. 
per 
sj.ft. 

7.9 

250 

Ibs. 
per 
sq.  ft. 

300 
Ibs. 
per 
sq.ft. 

5 

3.95 

10.5 

9.0 

6.3 

5.3 

6 

3.29 

0.10 

0.03 

11.0     8.8 

7.3     6.3     5.5 

4.4 

3.7 

7 

2.82  ' 

0.14 

0.04 

8.1     6.4     5.4     4.6  j   4.0 

3.2 

2.7 

8 

2.47 

0.18 

0.04 

6.2     4.9     4.1     3.5!   3.1 

2.5     2.1 

9 

2.20  ! 

0.23 

0.05 

4.9     3.9     3.3     2.8     2.4 

2.0     1.6 

10 

1.98  ; 

0.28 

0.05 

4.0 

3.2     2.6     2.3     2.0 

1.6 

1.3 

11 

1.80 

0.34 

0.06 

3.3 

2.6 

2.2     1.9 

1.7 

1.3  I~U 

12 

1.65 

0.40 

0.06 

2.8 

2.2 

1.8     1.6 

1.4 

1.1 

.9 

13 

1.52 

0.47 

0.07 

2.3 

1.9 

1.6     1.3 

1.2 

.9 

.8 

14 

1.41 

0.55 

0.07 

2.0 

1.6 

1.3 

1.1 

1.0 

.8 

.7 

15 

1.32 

0.63 

0.08 

1.8 

1.4 

1.2 

1.0 

.9 

'   .7 

.6 

16 

1.24 

0.71 

0.08 

1.6     1.2 

1.0      .9 

.8 

.6       .5 

17 

1.16 

0.80 

0.09 

1.4     1.1 

.9 

.8 

.7 

.5       .5 

18 

1.10 

0.90 

0.09 

1.2     1.0 

.8 

.7 

.6 

.5       .4 

19 

1.04 

1.00 

0.10 

1.1  i     .9 

.7 

.6 

.5 

.4       .4 

20 
21 

.99 
.94 

1.11 
1.22 

0.10 
0.11 

1.0 
.9 

.8 
.7 

.7 
.6 

.6 
.5 

.5 
.4 

A 

A 

A 

.3 
.3 

22 

.90 

1.34 

0.11 

.8 

.7      .5 

.5 

.4 

.3 

.3 

23 

.86 

1.47 

0.12 

.7 

.6 

.5 

.4 

.4 

.3 

.2 

24 

.82 

1.60 

0.12 

.7 

.5 

.4       .4 

.3 

.3 

.2 

UNION     IRON     MILLS' 

5-INCH    EYEBEAM,   No.    11,   HEAVY, 

13  LBS.  PER  FOOT. 

Depth,  5".     Width  of  Flanges,  2.91".    Thickness  of  Web,  0.405". 

Maximum  fiber  strain  =  12000  Ibs.  per  square  inch. 

Distance  between 
supports,  in  feet. 

:pl 

ijl 

Deflection  under  this 
load,  in  inches. 

Weight  of  beam,  in 
tons  of  2000  Ibs. 

Proper  distance,  in  feet,  center  to  center 
of  beams,  for  Safe  Loads  of 

100 

Ibs. 
par 

sq.ft. 

125 
Ibs. 

150 
Ibs. 
per 
sq.ft. 

175 
Ibs. 
per 

sq.ft. 

200 
Ibs. 
per 

sq.ft. 

9.1 

250 
Ibs. 
per 

7.3 

300 
Ibs. 
per 

sq.  ft. 

6.1 

5 

4.55 

0.07 

0.03 

18.2 

14.6 

12.1 

10.4 

6 

3.79 

0.10 

0.04 

12.6 

10.1 

8.4 

7.2 

6.3     5.1 

4.2 

7 

3.25 

0.14 

0.05 

9.3 

7.4 

6.2 

5.3 

4.6 

3.7 

3.1 

8 

2.85 

0.18 

0.05 

7.1 

5.7 

4.8     4.1 

3.6 

2.9 

2.4 

9 

2.53 

0.23 

O.OG 

5.6 

4.5 

3.7     3.2 

2.8 

2.2 

1.9 

10 

2.28 

0.28 

0.07 

4.6 

'  3.6 

3.0     2.6 

2.3 

1.8 

1.5 

11 
12' 
13 

2.07 
1.90 
1.75 

0.34 
0.40 
0.47 

0.07 
0.08 
0.08 

3.8 
3.2 

2.7 

3.0 
2.5 

2.2 

2.5 

2.1 
1.8 

2.1 
1.8 
1.5 

1.9 
1.6 
1.3 

1.5 
1.3 
1.1 

1.3 
1.1 
.9 

14 

1.63 

0.55 

0.09 

2.3 

1.9 

1.6 

1.3 

1.2 

.9 

.8 

15 

1.52 

0.63 

0.10 

2.0 

1.6 

1.4 

IwB 

1.0 

.8 

.7 

16 

1.42 

0.71 

0.10 

1.8 

1.4 

1.2 

1.0 

.9 

.7 

.6 

17 

1.34 

0.80 

0.11 

1.6 

1.3 

1.0 

.9 

.8 

.6 

.5 

18 

1.26 

0.90 

0.12 

1.4 

1.1 

.9!     .8 

.7 

.6 

.5 

19 

1.20 

1.00 

0.12 

1.3 

1.0 

.8      .7 

.6 

.5 

.4 

20 

1.14 

1.11 

0.13 

1.1       .9 

.8 

.7 

.6 

.5 

.4 

21 

1.08 

1.22 

0.14 

1.0 

.8 

.7 

.6 

.5 

.4 

.3 

22 

1.03 

1.34 

0.14 

.9 

.8 

.6 

.5 

.5 

.4 

.3 

23 

.99 

1.47 

0.15 

.9 

.7 

.6 

.5 

.4 

.3 

.3 

24 

'4  

.95 

1.60 

0.16 

.8 

.6 

i 

.5 

.5 

.4 

.3 

.3 
i 

UNION     IRON     MILLS1 

4-INCH    EYEBEAM,   No.    12,   LIGHT, 
8  LBS.  PER  FOOT. 

Depth,  4".    Width  of  Flanges,  2.48".     Thickness  of  Web,  0.23". 
Maximum  fiber  strain  =  12000  Ibs.  per  square  inch. 

jl 
•    II 

till 

fei 

'a  .2 

ii 

i~~ 

Proper  distance,  in  feet,  center  to  center 
of  beams,  for  Safe  Loads  of 

100 

Ibs. 
par 
sq.  ft. 

125 
Ibs. 
per 
sq.  ft. 

150 

Ibs. 
per 
sq.ft. 

175 
Ibs. 
per 
sj.ft. 

200 

Ibs. 

250 
Ibs. 

300 
Ibs. 
per 
sq.ft. 

I 
I 

5 

2.48     0.09   0.02 

9.9 

7.9     6.6 

5.7 

5.0 

4.0 

3.3 

6 

2.07 

0.13   0.02 

6.9 

5.5 

4.6 

3.9 

3.5 

2.8 

2.3 

7 

1.77     0.17 

0.03 

5.1 

4.0 

3.4 

2.9 

2.5 

2.0 

1.7 

8 

1.55     0.22 

0.03 

3.9 

3.1     2.6 

2.2 
1.8 

1.9 

1.6 

1.3 

1.0 

9 

1.38     0.28 

0.04 

3.1 

2.5 

2.0 

1.5 

1.2 

10 
11 

1.24 
1.13 

0.35 
0.42 

0.04 
0.04 

2.5 

2.1 

2.0 
1.6 

1.7 
1.4 

1.4 
1.2 

1.2 
1.0 

1.0 

.8 

.8 
.7 

12 

1.03 

0.50 

0.05 

1.7 

1.4 

1.1 

1.0 

.9 

.7 

.6 

13 

0.95 

0.59 

0.05 

1.5 

1.2 

1.0 

.8 

.7 

.6 

.5 

14 

0.89 

0.68 

0.06 

1.3 

1.0 

.8 

.7 

»    -6 

.5 

.4 

15 

0.83 

0.78 

0.06 

1.1 

.9 

.7 

.6 

.6 

.4 

.4 

16 

0.78 

0.89 

0.06 

1.0 

.8 

.6 

.6 

.5 

.4 

.3 

17 

0.78 

1.01 

0.07 

.9 

.7      .6      .5 

.4 

.3 

.3 

18 

0.69 

1.13 

0.07 

.8 

.6      .5 

.4 

.4 

.3 

.3 

19 

0.65 

1.26   0.08 

.7 

t 

.5      .4 

.3 

.3 

.2 

2 

53                                                   « 

—  I 
UNION     IRON     MILLS' 

4-INCH 

EYEBEAM,   No.    12,   HEAVY, 

10  LBS.  PER  FOOT. 

Depth,  4".    Width  of  Flanges,  2.63".    Thickness  of  Web,  0.88". 

Maximum  fiber  strain  =  12000  Ibs.  per  square  inch. 

•5^-jj 

I 

a 

Proper  distance,  in  feet,  center  to  center 

Jl 

fill 

»  •§ 

1§ 

of  beams,  for  Safe  Loads  of 

If 

^15 

5-2 

"o  ,_ 

100 

125 

150 

175      200 

250 

300 

ISff 

'•llf 

3  « 

Ibs. 

Ibs. 

Ibs. 

Ibs.       Ibs. 

Ibs. 

Ibs. 

1  1* 

sill 

1° 

|| 

£5, 

per       per 

sq.ft.    sq.ft. 

per       per       per       per 
sq.  ft.    sq.  ft.    sq.  ft.  j  sq.  ft. 

5 

2.80 

0.09 

0.03 

11.2 

9.0     7.5 

6.4 

5.6 

4.5 

3.7 

6 

2.33 

0.13 

0.03 

7.8 

6.2:   5.2 

4.4 

3.9     3.1 

2.6 

7 

2.00 

0.17 

0.04 

5.7     4.6 

3.8 

3.3 

2.9     2.3 

1.9 

8 

1.75 

0.22 

0.04 

4.4 

3.5     2.9 

2.5 

2.2     1.8     1.5 

9 

1.56 

0.28 

0.05 

r 

3.5     2.8     2.3|   2.0 

1.7     1.4     1.2 

10 

1.40 

0.35 

0.05 

2.8     2.2 

1.9 

1.6 

1.4 

1.1 

.9 

11 

1.27 

0.42 

0.06 

2.3     1.8 

1.5 

1.3 

1.2 

.9 

.8 

12 

1.17 

0.50   0.06 

2.0 

1.6 

1.3 

1.1 

1.0 

.8 

.7 

13 

1.08 

0.59 

0.07 

1.7 

1.3 

1.1 

.9 

.8 

.7 

.6 

14 

1.00 

0.68 

0.07 

1.4- 

1.1 

1.0 

.8 

.7 

.6 

.5 

1 

15 

0.93 

10.78   0.08 

1.2 

1.0 

.8 

.7 

.6 

.5 

.4 

16 

0.88 

0.89  i  0.08 

111 

.9 

.7 

.6 

.6 

.4 

.4 

17 

0.82 

1.01   0.09 

1.0 

.8 

.6 

.6 

.5 

.4 

.3 

18 

0.78 

1.13 

0.09 

.9 

.7 

.6 

.5 

.4 

.3 

.3 

19 

0.74 

1.26 

0.10 

,8 

.6      .5 

.4 

.4 

.3 

.3 

54 

UNION     IRON     MILLS' 

3-INCH    EYEBEAM,   No.    13,   LIGHT, 
7  LBS.  PER  FOOT. 

Depth,  3".    Width  of  Flanges,  2.32".    Thickness  of  Webv  0.19". 
Maximum  fiber  strain  =  12000  Ibs.  per  square  inch. 

M 

J  .3 
1  £ 

•M  IT 

Safe  load,  uniformly 
distributed,  (includ- 
ing weight  of  beam,) 
in  tons  of  2000  Ibs. 

P  P  1  Deflection  under  this 
£Q  to  1  l<>a(i,  in  inches. 

a 

"s£ 

»  5 

S3 
£_ 

Pro 

100 

Ibs. 
per 
sq.  ft. 

per  dis 
of  b 

125 
Ibs. 

41 

tance, 
earns, 

150 

Ibs. 
per 
sq.ft. 

4.4 
3.0 

2.2 
1.7 
1.4 

1.1 
.9 
.8 
.6 

.6 

in  fee 
forSa 

175 
Ibs. 
per 
4.  ft. 

,  cente 
?e  Loa 

loo 

Ibs. 
per 
sq.ft. 

r  to  c< 
Is  of 

250 
Ibs. 
per 
sq.ft. 

mter 

~300 

Ibs. 
per 

sq.ft. 

5 
6 

1.65 
1.37 

0.02 
0.02 

6.6 
4.6 

5.3 
3.7 

3.8 
2.6 

3.3 
2.3 

2.6 

1.8 

T3 
1.0 

.8 

.7 
.5 
.5 

:4s 

2.2 

1.5 

1.1 

n 

\7 

.5 
.5 
.4 
.3 
.3 

7 
8 
9 

10 
11 
12 
13 

14 

1.18 
1.03 
0.92 

0.82 
0.75 
0.69 
0.63 
0.59 

0.23 
0.29 
0.37 

0.46 
0.56 
0.67 
0.78 
0.91 

0.02 
0.03 
0.03 

0.04 
0.04 
0.04 
0.05 
0.05 

3.4 
2.6 
2.0 

1.6 
1.4 
1.2 
1.0 

.8 

2.7 
2.1 
1.6 

1.3 
1.1 
.9 

.8 
.7 

1.9 
1.5 

1.2 

.9 

.8 
.7 
.6 
.5 

1.7 
1.3 
1.0 

.8 

i 
i 

UNION    IRON    MILLS' 

3-INCH    EYEBEAM,   No.    13,    HEAVY, 
9  LBS.  PER  FOOT. 

Depth,  3".    Width  of  Flanges,  2.52".    Thickness  of  Web,  0.39". 
Maximum  fiber  strain  =  12000  Ibs.  per  square  inch. 

Distance  between 
supports,  in  feet. 

Safe  load,  uniformly 
distributed,  (includ- 
ing weight  of  beam,) 
in  tons  of  2000  Ibs. 

Ij 

a 

11 

a 
•JJ 

^5 

ILi 

s* 

Proper  di 
oft 

stance,  in  feet,  center  to  center 
earns,  for  Safe  Loads  of 

100 

Ibs. 
per 

sq.  ft. 

125 

Ibs. 
per 
sq.  ft. 

150 

Ibs. 
per 
sq.  ft. 

175 
Ibs. 
per 

sq.ft. 

200 
Ibs. 
per 

sq.  ft. 

3.8 
2.6 

1.9 
1.5 

1.2 

.9 
.8 
.7 
.6 
.5 

250 

Ibs. 
per 
sq.ft. 

300 
Ibs. 

SqP\ 

5 
6 

1.89 
1.57 

0.12 
0.17 

0.02 
0.03 

7.6 
5.2 

3.9 
3.0 
2.3 

1.9 
1.6 
1.3 
1.1 
1.0 

6.0 
4.2 

5.0 
3.5 

4.3 

3.0 

3.0 
2.1 

2.5 

1.7 

7 
8 
9 

10 
11 
12 
13 
.       14 

1.35 
1.18 
1.05 

0.94 
0.86 
0.79 
0.73 
0.67 

0.23 
0.29 
0.37 

0.46 
0.56 
0.67 
0.78 
0.91 

0.03 
0.04 
0.04 

0.05 
0.05 
0.05 
0.06 
0.06 

3.1 
2.4 
1.9 

1.5 
1.2 
1.1 
.9 
.8 

2.6 
2.0 
1.6 

1.3 
1.0 

.9 
.7 
.6 

2.2 
1.7 
1.3 

1.1 

.9 
.8 
.6 
.5 

1.5 
1.2 
.9 

.8 
.6 
.5 
.4 
.4 

1.3 
1.0 

.8 

.6 
.5 
.4 
.4 
.3 

8                                                  55                                                 ° 

EXPLANATION    OF    TABLES    ON    THE 

PROPERTIES    OF    UNION    IRON    MILLS' 

EYE  AND  DECK  BEAMS,  CHANNEL 

BARS,    ANGLE,    STAR    AND 

TEE    IRONS. 

Pages  62  to  69,  inclusive. 

The  tables  on  I  Beams,  Deck  Beams  and  Channel  Bars  are 
calculated  for  the  minimum  and  maximum  weight  to  which  the 
various  shapes  can  be  rolled.  The  lithographed  plates  indicate 
the  manner  in  which  the  enlargement  of  the  section  takes  place, 
and  column  7  in  tables  gives  the  increase  of  thickness  of  web 
for  each  pound  increase  of  weight  of  beam  or  channel.  The 
width  of  flanges  is  increased  the  same  amount  as  the  thickness 
of  web. 

Angle  Irons  are  increased  in  weight  in  the  manner  indicated 
by  Fig.  4  on  page  23,  the  size  corresponding  with  the  least 
thickness,  and  increasing  somewhat  with  the  increase  of  thick- 
ness, but  some  of  the  heavier  weights  of  a  few  of  the  shapes 
are  rolled  in  special  finishing  grooves,  whereby  the  exact  size  is 
obtained  for  a  thickness  greater  than  the  minimum.  In  the 
tables,  for  the  sake  of  uniformity,  it  was  assumed  generally  that 
the  size  corresponds  with  the  least  thickness  only,,  and  the 
increase  of  weight  is  obtained  in  the  manner  indicated  by  the 
above  mentioned  Fig.  4,  page  23. 

Beams,  Channels  and  Angle  Irons,  may  be  rolled  to  any 
weight  intermediate  between  the  minimum  and  maximum 
weights  given.  Each  shape  of  Star  and  T  Iron,  however, 
can  be  rolled  to  one  weight  only. 

Columns  11  and  13  in  the  tables  for  beams  and  channels  give 
coefficients,  by  the  help  of  which  the  safe  uniformly  distributed 
load  for  any  beam  or  channel,  and  for  any  span  length,  can  be 
readily  and  quickly  determined.  To  do  this,  it  is  only  necessary 
to  divide  the  coefficient  given  by  the  span  or  distance  between 
supports,  in  feet,  and  multiply  by  1000.  If  the  weight  of  the 
beam  or  channel  is  intermediate  between  the  minimum  and 

£B  5g 


maximum  weights  given,  add  to  the  coefficient  for  the  minimum 
weight,  the  value  given  in  columns  12  or  14  (for  one  pound 
increase  of  weight)  multiplied  by  the  number  of  pounds  the  beam 
or  channel  is  heavier  than  the  minimum. 

If  a  beam  or  channel  is  to  be  selected,  (as  will  usually  be  the 
case,)  intended  to  carry  a  certain  load  for  a  length  of  span 
already  determined  on,  it  will  be  most  convenient  to  ascertain 
the  coefficient  which  this  load  and  span  will  require,  and  refer  to 
the  table  for  a  beam  or  channel  having  a  coefficient  as  large  as 
this.  The  coefficient  is  obtained  by  multiplying  the  load,  in 
pounds  uniformly  distributed,  by  the  span  length  in  feet,  and 
dividing  by  1000. 

In  case  the  load  is  not  uniformly  distributed,  but  is  concen- 
trated at  the  middle  of  the  beam  or  channel,  multiply  the  load 
by  2,  and  then  consider  it  as  uniformly  distributed.  The  deflec- 
tion will  be  y^jths  of  the  deflection  by  this  load. 

If  the  load  is  neither  uniformly  distributed  nor  concentrated 
at  the  middle,  obtain  the  bending  moment.  This,  multiplied  by 
0.008  will  give  the  required  coefficient. 

If  the  loads  for  which  the  beams  or  channels  are  to  be  pro- 
portioned, are  quiescent,  the  coefficients  for  a  fiber  strain  of 
12000  Ibs.  per  square  inch  should  be  used ;  but  if  moving  loads 
are  to  be  provided  for,  the  coefficients  fo*r  10000  Ibs.  fiber  strain 
should  be  taken.  Inasmuch  as  the  effects  of  impact  may  be 
very  considerable,  (the  strains  produced  in  an  unyielding  inelastic 
material  by  a  load  suddenly  applied,  being  double  those  produced 
by  the  same  load  in  a  quiescent  condition,)  it  will  sometimes  be 
advisable  to  use  still  smaller  fiber  strains  than  10000.  The  co- 
efficients for  these  can  readily  be  determined  by  proportion. 
Thus,  for  a  fiber  strain  of  8000  Ibs.  per  square  inch,  the  coefficient 
will  equal  the  coefficient  for  10000  Ibs.  fiber  strain  multiplied 
by  ^-ths. 

The  table  on  the  properties  of  Union  Iron  Mills'  Angle  Irons 
requires  explanation  only  relative  to  the  angles  with  unequal 
legs,  to  which  the  latter  half  of  the  table  applies.  It  will  be 
observed  that  two  values  are  given,  in  the  case  of  each  angle, 
for  the  distance  of  center  of  gravity  from  outside  of  flange,  the 
moment  of  inertia,  the  moment  of  resistance  and  the  radius  of 


67 


gyration  of  the  section.  The  first  or  larger  value  invariably 
refers  to  a  neutral  axis  parallel  to  the  smaller  flange,  and  to  the 
distance  between  the  center  of  gravity  and  the  outside  of  this 
flange,  and  the  second  or  smaller  value  to  a  neutral  axis  parallel 
to  the  larger  flange,  and  to  the  distance  between  the  center  of 
gravity  and  the  outside  of  this  flange.  For  each  position  of  the 
neutral  axis  there  will  be  two  moments  of  resistance,  since  the 
distance  between  the  neutral  axis  and  the  extreme  fibers  has  a 
different  value  on  one  side  of  the  axis  from  what  it  has  on  the 
other.  The  moment  of  resistance  given  in  table  is  the  smaller 
of  these  two  values,  and  the  fiber  strain  calculated  from  it,  will 
therefore  give  the  larger  of  the  two  strains  in  extreme  fibers, 
(since  these  strains  are  equal  to  the  bending  moment  divided  by 
the  moment  of  resistance  of  the  section).  The  left  hand  figures 
in  each  column  refer  to  the  minimum  weight  of  angle,  and  the 
right  hand  figures  to  the  maximum  weight,  throughout  the  table. 

The  table  on  the  properties  of  Union  Iron  Mills'  T  Irons 
is  modeled  after  the  foregoing,  and  will  therefore  scarcely 
require  explanation.  The  horizontal  portion  of  the  T  is  called 
the  flange  and  the  vertical  portion  the  stem.  In  the  case  of  the 
neutral  axis  parallel  to  the  flange,  there  will  be  two  moments  of 
resistance,  and  the  least  is  given;  but  in  the  case  of  the  neutral 
axis  coincident  with  stem,  there  is  only  one  moment  of  resistance. 
In  calculating  the  table,  the  flange  and  stem  of  the  T's  were 
considered  as  rectangles  of  equal  area  as  the  actual  section,  and 
the  figures  given  are  therefore  approximations  only,  though  very 
close  ones. 

No  approximations  have  entered  into  the  calculations  of  any 
of  the  other  tables,  and  the  figures  given  may  be  relied  upon  as 
accurate. 

The  use  of  the  radii  of  gyration  will  be  explained  in  connec- 
tion with  the  table  on  the  strength  of  wrought  iron  columns. 
The  moment  of  resistance  is  used  to  determine  the  fiber  strain  in 
a  beam  or  other  shape  iron  subjected  to  bending  or  transverse 
strains,  by  simply  dividing  the  same  into  the.  bending  moment, 
expressed  in  inch  pounds.* 

The  15th  column  in 'the  table  on  the  Properties  of  Union  Iron 
Mills'  Channels,  giving  the  distance  of  the  center  of  gravity  of 


58 


channels  from  outside  of  web,  is  used  to  obtain  the  radius  of 
gyration  for  columns  or  struts  consisting  of  two  channels  latticed, 
as  represented  by  Fig.  1,  page  26,  in  the  case  of  the  neutral  axis 
passing  through  the  center  of  the  section  parallel  to  the  webs  of 
the  channels.  This  radius  of  gyration  is  equal  to  the  square  root 
of  the  distance  between  the  center  of  gravity  of  the  channel  and 
the  center  of  the  section. 

EXAMPLES   OF   APPLICATION   OF   TABLES. 

I.  What  load,  uniformly  distributed,  will  a  10"  beam  'carry, 
weighing  40  Ibs.  per  foot,  and  measuring  14  feet  between  sup- 
ports, allowing  a  fiber  strain  of  12000  Ibs.  per  square  inch  ? 

Answer  :  By  table,  C,  for  a  10"  beam,  40  Ibs.,  =  240  -f  10  X 
4  =  280,  therefore  L  =—  )0  *  28°  =  20000  Ibs.,  including 
weight  of  beam. 

II.  What  beam  will  be  required  to  carry  36000  Ibs.,  uniformly 
distributed  over  a  span  of  16  feet  between  supports,  same  fiber 

strain  ? 

1L          16  X  36000         K-c     ,  .  , 
Answer:    C  required  =  -^  = -^ =  576,  which 

calls  for  a  15"  beam,  52  Ibs.  per  foot. 

III.  A  light  4"  X  3"  angle  iron,  weighing  8.3  Ibs.  per  foot, 
spanning  4  feet,  is  loaded  with  1000  Ibs.  at  center :   what  will  be 
the  maximum  fiber  strain  if  the  4/;  flange  is  in  a  vertical  position  ? 

Answer:  By  table,  moment  of  resistance  =  1.46.  Bending 
moment  =  12000  inch  pounds.  Therefore  maximum  fiber  strain= 

120^Q    =  8220  *lbs.,  occurring   in  the  fibers  furthest  from  the 
1.46 

neutral  axis,  i,  e.,  at  the  end  of  the  long  flange. 

SPECIAL    CASES   OF   LOADING. 

I.  Beam  loaded  at  a  point  distant  "-a"  feet  from  the  left 
hand  and  "b"  feet  from  the  right  hand  support,  by  a  single 
load  P. 

1  =  length  of  beam  between  supports  =  a  -|-  b. 

59 


Maximum  bending  moment,  neglecting  dead  weight  of  beam, 
occurs  at  point  of  application  of  the  load  and  =  —  — 

I2 
P  =  load  given  in  tables  X 


8ab 
Pressure  or  reaction  at  left  hand  support  =  P  —,  and  at  right 

hand  support  ==  P  -p 

II,     Beam  unsupported  at  one  end  and  held  horizontally  at 
the  other,  1  representing  the  length  of  beam  from  end  to  support. 

If  loaded  by  a  uniformly  distributed  load  W : 

W  1 

bending  moment  occurs  at  support  and  =  — ^ — 


W=  load  given  in  tables  X  X»  and  tne  deflection  =  that  of 
the  tables  X  2.4. 

If  loaded  with  a  single  load  P  at  its  extremity  : 
Maximum  bending  moment  occurs  at  support  and  =  PI. 
P  =  load  given  in  tables  X  ^>  and  the  deflection  that  of 
tables  X  3.2. 

GENERAL  FORMULAE  ON  THE  FLEXURE  OF  BEAMS 
OF  ANY  CROSS-SECTION. 

Let  A  =  area  of  section, 
1  =  length  of  span, 
W  =  load,  uniformly  distributed, 
M  =  bending  moment, 
d  =  depth  of  beam,  out  to  out, 
n  =  distance  of  center  of  gravity  of  section,  from  top  or 

from  bottom, 
s  =  strain  per  square  inch  in  extreme  fibers  of  beam,  either 

top  or  bottom, 
D  =  maximum  deflection, 
I  =  moment  of  inertia  of  section, 
R  =  moment  of  resistance, 
r  =  radius  of  gyration, 
E  =  modulus  of  elasticity, 

(assumed  =  2600QOOO  for  wrought  iron  in  tables.) 


Then  R  = 


~~r~        R 

8  =T  8  Q 

w=- 


_      Win          _wi_ 
81  8  R 

5  Wl3  for  beam  supported  at  both   ends  and  uni- 

384  El  formly  loaded, 

_      PI3  for  beam  supported  at  both  ends  and  loaded 

~  48  El  by  a  single  load  P  at  middle, 

_     Wl3  for  beam  held  horizontally  at  one  end  only 

8  El  and  uniformly  loaded, 

PI3  for  beam  held  horizontally  at  one  end  only 

3  El  and  loaded  with  a  single  load  P  at  the  other. 


VALUES  OF  /  AND  Jt  FOR  USUAL  SECTIONS. 

Rectangle ;    h  =  hight,  b  =  base ;    for  neutral  axis  through 
center  of  gravity,  parallel  to  base,  I  =  ,  R  = — ^— - ;  for 

bh3 

neutral  axis  coincident  with  base,  I  =  — ^ — . 

o 

Triangle ;  h  =  hight,  b  =  base ;  for  neutral  axis  through  center 
of  gravity  (i.  e.,  distant  ^  h  from  base),  parallel  to  base,  I  = 

-      -,  R  =  -        ;    for  neutral  axis  coincident  with  base,  I  = 

OD  min.        fA. 

bh3  bh3 

-.    -.;  for  neutral  axis  through  apex,  parallel  to  base,  I  = 


4 

Circle  ;    d  =  diameter,  TT  =  3.1416;   for  neutral  axis  through 


7T   (\  3 

center,  I  =        -  =  0.0491  d*,  R  =-=-  =  0.0982  d». 


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3                                                                                                                                      f. 

UNION  IKON  MILLS'  ANGLE  IRONS. 

Weights   per  Foot  corresponding  to   thicknesses   varying  by  Ty". 
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14.4 

29.2 
19.5 
17.0 
15.8 

31.7 

.. 

34.2 

.... 

.. 

•• 

9.5 

8.3 
7.7 

7.2 
6.5 
5.9 
5.4 

4.8 
4.3 
36 

11.2 
9.7 
9.0 

8.4 
7.7 
7.0 
6.4 

56 

2.1 
..     1.8 
1.0  1.5 

0.9    1.4 
0.8    1.2 
06i  09 

3*5 

8.1 
2.8 
2.4 
2.0 

1.8 
1  6 

5.9 
5.4 
4.9 
4.5 

4.0 
3.5 
3.0 

8.0 

7.3 

•  • 

.  .  j  .  . 

•  • 

50 

j 
j 

i 

UnequalLegs 
6     x4 
5     x4 
5     x3X 

5     x3  " 

4     x3>£ 
4     x3 
3>^x3 
3>4X2 

3     x2^ 
3     x2 
2X  x  2 
2  "xl% 
,. 

.... 

10.8 
10.2 
9.5 

13.9 
12.7 
11.9 
11  ?, 

16.0  1.8.1 
14.5  16.4 
13.7  15.5 
12.9  14.5 

20.222.324.4 
18.3  20.2  22.0 
17.2  19.0  20.8 
16.2  17.9  19.5 

15.2  1^7  1C.3 
14.1  15.6  17.0 
13.1  14.4  15.8 

26.4 

.  .  1  .  . 

•• 

•• 

8.910.5  12.0 

8.3|  9.7  11.2 
7.7  9.010.4 
6.4  7.4    8.5 

6.7  7.8   9.0 
6.0  7.1  '••  8.1 
5.4   6.4   7.3 
40 

13.6 
12.7 
11.7 

4.2 

4.4 
4.0 
3.5 
2.6 

5.3 

5.5 
5.0 
4.5 
3.3 

•• 

•• 

•• 

•• 

•• 

|       1 

.  —  if 

<5 

8 

PROPERTIES    OF     UNION 

IRON    MILLS' 

T    IRONS. 

The  moments  of 

inertia  and  resistance,  and  radii  of  gyration,  in  this 

table,  are  close  approximations  only. 

The  table  does  not  include  all  sizes  manufactured. 

w 

| 

ij 

|J 

111 

f3 

•s|  :||5 

1-1*5*1! 

all 

I'glJl  |a 

gll 

sT 
m 

1*1^1- 

II? 

111 

5     X3 

13 

3.90  !  0.73 

2.5      1.1 

0.80 

5.7     !  2.3 

1.21 

5     X25£ 

101* 

3.08    0.58 

1.4      0.71 

0.66 

4.6     i  1.8 

1.21 

-4)^X33-2 

15 

4.50  1  1.13 

5.2      2.18 

1.07 

3.9     ;  1.7 

0.93 

4     X5      14 

4.20    1.57 

10.5      3.05 

1.57 

2.7     |  1.4 

0.80 

4     X4X  13j^ 

4.05  i  1.37 

7.8      2.48 

1.39 

2.7       1.4 

0.82 

4     X4  "  12 

3.60  !  1.18 

5.4    i  1.91 

1.22 

2.6       1.3 

0.84 

4     X3        ^ 

2.78  ,  0.80 

2.1     |  0.96 

0.87 

2.3       1.1 

0.90 

4     X%%    ly2 

2.25  ;  0.62 

1.1        :    0.60 

0.70 

2.0       1.0 

0.93 

4     X2        6K 

1.95  l  0.46 

0.54     0.35 

0.53 

1.8     1  0.91 

0.96 

3l£X4      11)£ 

3.38    1.24 

5.15  i  1.87 

1.23 

1.8       1.00 

0.72 

3)^X3^  10 

8.00  !  1.04 

3.34  !  1.36 

1.05 

1.6       0.93 

0.73 

3^X3        9>^ 

2.78  |  0.85 

2.14     1.00 

0.88 

1.6       0.93 

0.77 

3     X4      1214  3.68  !  1.35 

5.55  '12.10 

1.24 

1.8     !  0.87 

0.60 

3     X3^'  11% 

3.53  j  1.15 

3.93     1.67 

1.06 

1.4       0.92 

0.62 

3     X3        7.6 

2.28  i  0.90 

1.89     0.90 

0.91 

0.94     0.63 

0.64 

3     X2>£    6 

1.80  !  0.69 

0.96  ;  0.53 

0.73 

0.77     0.51 

0.66 

2^X3    :   6^ 

1.95  !  0.96 

1.66     0.81 

0.93 

0.50     0.40 

0.51 

2KX2%-    6.6 

1.98    0.86 

1.39  !  0.74 

0.84 

0.55     0.44 

0.53 

2)^X2^    5.4 

1.62    0.75 

0.91     0.43 

0.75 

0.46     0.37 

;  0.53 

2^>Xl*4i   3 

0.90  i  0.30 

0.09     0.10 

0.32 

0.33     0.26 

0.61 

PROPERTIES    OF    UNION 

IRON    MILLS' 

STAR    IRONS. 

Size. 
Inches. 

Weight      Thickness  in  \                       Inertia0       Moment  of     Radius  of 
perfoot.       If^sat           Area.      |  neutral  ^  ;   Resistance,      Gyration, 
r  Lb?        End  and  Root  i     Sq.  In.    !  +;,,.«'  M«t«.    neutral  ans  neutral  axis 

of  Flange.    |                  I  ^ 

gravity       as  Before.      as  before. 

4     X4 

12 

M  —  T9u  !     3.60    , 

2.32          1.16 

0.81 

3%  X3^ 

91 

4   %—IA     2.85  ; 

1.49          0.85 

0.72 

3     X3 

7» 

4     T56-M  i    2.18 

0.82          0.55 

0.61 

2M  X2^ 

4    A  —  -H      I.® 

0.45          0.36 

0.52 

2     ><2 

3^ 

4     U'—M       1.13 

0.20      i    0.20 

0.43 

O 

&. 

3      tV  —  A  >    0.69    i 

0.065         0.087 

0.31     . 

69 

^ 

EXPLANATION  OF  TABLE  ON  RIVETED 
GIRDERS. 

Riveted  girders  are  used  in  cases  where  rolled  I  Beams  are 
insufficient  to  carry  the  load.  On  page  23  of  the  lithographed 
plates  will  be  found  illustrations  of  various  forms  of  riveted 
girders.  The  sections  with  single  webs  are  more  economical 
than  those  with  double  webs  (box  girders),  but  the  latter  are 
stiffer  laterally,  and  should  always  be  used  where  the  proportion 
of  length  of  span  to  width  of  top  flange  is  great  and  the  girder 
is  not  held  in  position  sideways.  This  proportion  of  length  to 
width  should  not  exceed  twenty,  without  making  provision  for 
such  increase  by  an  addition  of  metal  in  the  compression  flange 
beyond  that  required  by  the  table. 

The  web  of  the  girder  must  be  made  of  such  thickness  that 
there  will  be  no  tendency  to  buckle,  and  that  the  vertical  shearing 
stress  per  square  inch  will  not  exceed  9000  Ibs.  This  shearing 
stress  is  obtained  by  dividing  half  the  load  upon  the  girder  by 
the  web  section.  The  first  condition  is  attained  when  this 

10000 

shearing  stress  does  not  exceed  d2       in  which  d  repre- 

h~~^ 


sents  the  depth  of  web  of  girder  and  t  its  thickness,  both  in 
inches.  Ordinarily  this  formula  gives  a  lower  strain  per  square 
inch  than  9000  Ibs.,  so  that  both  conditions  are  usually  attained 
when  the  first  is.  Instead  of  increasing  the  thickness  of  the 
web,  it  may  be  stiffened  also  by  means  of  vertical  angle  irons 
riveted  to  it  at  proper  intervals.  These  should  always  be  less 
than  the  depth  of  the  girder,  at  least  for  the  end  panels,  but 
towards  the  middle  of  the  girder  the  stiffeners  may  be  placed 
further  apart  or  entirely  omitted.  Stiffeners  '  should  always  be 
used  at  or  near  the  supports,  and  at  any  other  points  where  there 
is  a  concentration  of  heavy  loads. 

The  rivets  should  be  ^",  unless  the  girder  is  light,  when  $" 
may  be  sufficient.  The  spacing  ought  not  to  exceed  6"  and 
should  be  closer  for  heavy  flanges,  but  in  all  cases  it  should  be 
close  at  the  ends,  say  3"  for  a  distance  of  18"  to  24"  at  each  end. 


The  following  table  furnishes  a  ready  means  of  determining 
the  section  of  girder  necessary  to  carry  a  certain  load,  for  any 
span  length  from  10  to  39  feet,  inclusive. 

It  will  be  noticed  that  the  table  is  calculated  for  an  allowed 
fiber  strain  of  10000  Ibs.  per  square  inch,  while  the  tables  on 
rolled  beams  are  calculated  for  a  fiber  strain  of  12000  Ibs.  per 
square  inch.  This  reduction  in  the  allowed  strain  is  intended  to 
cover  the  loss  in  strength,  (somewhat  greater  than  the  loss  in  sec- 
tion,) due  to  the  rivet  holes,  and  the  riveted  girders  proportioned 
by  this  table,  will  be  found  to  be  of  about  the  same  strength 
as  the  rolled  beams,  proportioned  by  the  tables  applying  to  them. 
The  transverse  strength  of  the  web  is  neglected  in  the  table. 

The  term  flange,  as  applied  to  riveted  girders,  embraces  all 
the  metal  in  top  or  bottom  of  girder  exclusive  of  web  plate; 
or,  in  the  case  of  a  rolled  beam  or  channel,  with  top  and  bottom 
plates,  all  the  metal  exclusive  of  web  between  fillets. 

Girders  intended  to  carry  plastering,  should  be  limited  in  depth, 
out  to  out,  to  JTth  of  the  span  length  or  y2"  per  foot  of  this 
length,  otherwise  the  deflection  is  liable  to  cause  the  plastering 
to  crack. 

EXAMPLE   OF  APPLICATION   OF   TABLE. 

A  20;/  box  girder  is  to  carry  a  13"  brick  wall  equivalent  to  a 
weight  of  30  tons  over  a  space  20'  in  the  clear.  What  size  of 
girder  is  required? 

Answer :  The  value  of  the  coefficient  for  20'  span  and  20/7 
depth,  as  per  table,  =  300,  and  for  21'  span  and  20"  depth  = 
315.  The  span,  in  this  case,  may  be  assumed  at  20M5",  and  the 

coefficient  therefore  at  307.      Consequently  —     *, — =  9.21 

will  be  the  area  required  in  each  flange.  Making  the  top  and 
bottom  plates  12"  X  ¥&">  =  4.5  sq.  in.,  there  remain  4.7  sq.  in.  for 
the  two  angles,  =  8  Ibs.  per  foot  apiece.  Making  the  webs 

* 


20"  X  X",  the  shearing  stress  =  ~ g        g0     ^  /2   =  3000  Ibs. 

per   square   inch,   which   is   also   safe   against    buckling,   since 
10000  10000 

d2        =  (20) 2         =  3200  Ibs.,  allowed. 

h  3000  t2  3000  (X)2 

71 


RIVETED 

—  a 
GIRDERS. 

Coefficients  for  determining  the  area  required  in  flanges,  allow- 

ing 10000  Ibs.  per  square  inch  of 

gross  section  fiber  strain  : 

Multiply  the  load,  in  tons  of  2000 

Ibs., 

uniformly  distributed, 

by  the  coefficient,  and  divide  by 

1000;   the  quotient  will  be  the 

gross  area,  in  square  inches,  required 

for  each  flange. 

|t| 

Depth  of  Girder,  Out 

to  Out  of  Web,  in  Inches. 

J3  S^ 

12    14 

i 

i       ; 

&%  ~ 

16 

18    20   22 

24 

26 

28    30 

32    34   36 

10 

250 

214 

188 

167   150   136 

125 

115 

107  100 

94     88;   83 

11 

275 

:236 

206 

183   165   150 

138 

127 

118   110 

103     97     92 

12 

300 

|257 

2251200   180   164 

150 

138 

129  120 

113  106   100 

13 

325 

279 

2441217   195   177 

163 

150 

139   130 

122:115   108 

14 

350 

300 

263 

233  210   191 

175 

162 

150   140 

131   124   117 

| 

15 

375 

321 

281 

250  225  205 

188 

173 

161   150 

141  :  132   125 

16 

400 

343 

300 

267:240  218 

200 

185 

171   160 

150  i  141  1  133 

17 

425 

364 

319 

283   255  232 

213 

196 

182  !  170 

159   150  !  142 

18 

450 

386 

338 

300   270  245 

225 

208  i  193  i  180 

169  159   150 

19 

475 

|407 

356 

317  285  259 

238 

219  204   190 

178   168   158 

20 

500 

429 

375 

333   300  273 

250 

231 

214  200 

188   176   167 

21 

525 

450 

394 

350   315  286 

263 

242 

225  210 

197   185   175 

22 

550 

471 

413 

"367   330  300 

275 

254 

236  220 

206   194   183 

23 

575 

493 

431 

383   345  314 

288 

265 

246  i  230 

216  203   192 

24 

600 

514 

450 

400   360  327 

300 

,277 

257  240 

225  212  200 

I 

1 

25 

625 

536 

469 

417  375  341 

313 

!288 

268  250  : 

234  221   208 

26 

650 

557 

488 

433  390  355 

325 

300 

279  260  ' 

244  '229  217 

27 

675 

579 

506 

450  405  368 

338 

312 

289  j  270 

253  238  i  225 

28 

700 

600 

525 

467  420   382 

350 

323 

300  280 

263  247  233 

29 

725 

621 

544 

483  435   395 

363 

335 

311  290 

272  256:242 

30 

750 

643 

563 

500  450  409  : 

375 

346 

321   300 

281   265  250 

31 

775 

664 

581 

517  465  423 

388 

358 

332  310 

291   274  258 

32 

800 

686 

600  533  480  436 

400 

369 

343  320 

300  282  267 

33 

825 

707 

619 

550   495  450 

413 

381  : 

354  330 

309  291   275 

34 

850 

729  638 

567  510  464 

425 

392 

364   340 

319   300  283 

35 

875 

750  656 

583  525  l  477 

438 

404' 

375  '  350  ! 

328  '  309  :  292 

36 

900 

771 

675 

600  540  491 

450 

415 

386  360 

338   318   300 

37 

925 

793 

694; 

617  555  505' 

463 

427 

396  370' 

347   326  308 

38 

950 

814  713! 

633  570  518 

475 

438 

407  380 

856  335   317 

39 

r/,._. 

975 

836 

731 

650:585  532 

488 

450 

418  390 

366  344  325 

72                                                  ™ 

COLUMNS    AND    STRUTS. 
Explanation  of  tables,  pages  77  to  81,  inclusive. 

The  tables  on  Keystone  Octagon  and  Piper's  Patent  Rivetless 
Columns  give  the  areas  and  weights  corresponding  to  different 
thicknesses  of  metal.  Sections  of  these  columns  will  be  found 
'on  pages  13  and  14. 

As  it  is  .impossible  to  repaint  the  inner  surface  of  closed 
columns,  or,  at  best,  this  is  attended  with  much  difficulty  and 
expense,  such  columns  should  preferably  be  used  only  in  the 
interior  of  buildings,  where  the  changes  in  temperature  are  not 
considerable  and  the  air  is  comparatively  dry.  In  places  exposed 
to  the  extremes  of  temperature  and  unprotected  from  the  rain,  the 
paint  on  the  inner  surface  of  the  columns  will,  sooner  or  later, 
cease  to  be  a  protection  to  the  iron  from  the  moisture  of  the 
atmosphere,  corrosion  will  set  in,  and,  once  begun,  will  continue 
as  long  as  there  is  unoxidized  metal  left  in  the  column. 

Figures  1,  3  and  4,  on  page  26,  represent  types  of  columns  with 
open  sections,  which  admit  of  repainting  at  any  time,  and  are 
therefore  suitable  for  out-door  work. 

The  table  on  the  Ultimate  Strength  of  Hollow  Cylindrical 
Cast  and  Wrought  Iron  Columns  gives  the  strains  per  square 
inch  of  section  at  which  columns  will  fail,  for  various  propor- 
tions of  length  of  column  to  diameter. 

To  facilitate  the  use  of  the  table,  the  length  (=1)  is  ex- 
pressed in  feet,  and  the  diameter  ( =  d )  in  inches.  The 
diameter  to  be  assumed  is  the  mean  between  the  outside  and 
inside  diameters  of  the  section. 

Wrought  iron  columns  fail  either  by  deflecting  bodily  out  of 
the  straight  line,  or  by  the  buckling  of  the  metal  between  rivets 
or  other  points  of  support.  Both  actions  may  take  place  at  the 
same  time,  but  if  the  latter  occurs  by  itself,  it  is  an  indication 
that  the  rivet  spacing  or  the  thickness  of  metal  is  insufficient; 
provided,  however,  that  the  length  of  column  is  greater  than 
twelve  diameters,  as  columns  of  shorter  length  fail  generally 
by  the  buckling  of  the  metal.  The  rule  has  been  deduced 
from  actual  experiments,  that  the  distance  between  centers  of 
_ 


rivets  in  columns  should  not  exceed,  in  the  line  of  stress,  sixteen 
times  the  thickness  of  metal  of  the  parts  joined,  and  that  the 
distance  between  rivets  or  other  points  of  support  at  right  angles 
to  the  line  of  stress,  should  not  exceed  thirty  times  the  thickness 
of  metal. 

The  table  on  the  Ultimate  Strength  of  Wrought  Iron  Columns 
gives  the  strain  per  square  inch  of  section  at  which  columns  will  • 
fail,  for  various  proportions  of  length,  in  feet,  to  least  radius  of 
gyration,  in  inches.  This  table  should  be  used  for  columns  and 
struts  which  are  not  cylindrical,  such  as  those  represented  by 
Figures  1,  2,  3,  4  and  5,  on  page  26. 

If  the  column  or  strut  is  a  single  rolled  beam,  channel  or  other 
shape,  the  radius  of  gyration  will  be  found  in  the  foregoing 
tables  on  the  properties  of  Union  Iron  Mills'  Beams,  Channels,  etc. 

If  the  column  is  composed  of  two  channels  latticed,  as 
represented  by  Fig.  1,  on  page  26,  the  channels  are  usually 
placed  far  enough  apart  so  that  the  column  will  be  weakest  in 
the  direction  of  the  webs,  i.  e.,  with  neutral  axis  at  right  angles 
to  the  webs;  for  which  case  the  radius  of  gyration  of  the 
column  section  is  the  same  as  that  of  the  single  channel.  But  if 
the  radius  of  gyration  is  wanted  for  the  neutral  axis  through 
center  of  section  parallel  with  web,  obtain  first  the  distance 
between  center  of  gravity  of  channel  and  center  of  section,  by 
the  help  of  column  15  in  table  on  the  properties  of  Union  Iron 
Mills'  Channel  Bars;  the  square  root  of  this  distance  will  be  the 
radius  of  gyration  of  the  section. 

For  a  column  section  consisting  of  two  channels  with  a  beam 
between  them,  as  in  Fig.  3,  on  page  26,  it  is  necessary  to  obtain 
first  the  moment  of  inertia  of  the  section,  whence  the  radius  of 
gyration  is  found  as  the  square  root  of  the  quotient  of  the  moment 
of  inertia  divided  by  the  area  of  the  section.  This  moment  of 
inertia,  for  a  neutral  axis  through  center  of  beam  coincident  with 
web,  is  equal  to  the  sum  of  the  moments  of  inertia  of  the  beam 
and  channels,  as  per  tables  on  the  properties  of  these  shapes. 
The  moment  of  inertia  with  neutral  axis  through  center  at  right 
angles  to  web  of  beam,  is  found  by  adding  the  moment  of  inertia 
of  the  beam  for  this  position  of  the  axis,  as  per  tables,  to  the 
product  of  the  area  of  both  channels  multiplied  by  the  square 

m 


of  the  distance  of  the  center  of  gravity  of  the  channel  from 
the  center  of  the  section.  The  moment  of  inertia,  thus  obtained, 
is  approximate,  being  too  small  by  the  value  of  the  moment  of 
inertia  of  the  channels  with  reference  to  a  neutral  axis  through 
their  centers  of  gravity  parallel  to  the  web,  but  the  error  is  small 
and  on  the  safe  side. 

For  a  section  composed  of  three  beams,  as  represented  by 
Fig.  4,  page  26,  the  correction  for  this  approximation  can  be 
made,  since  the  moments  of  inertia  of  beams  with  reference  to 
an  axis  through  their  centers  of  gravity  parallel  to  (coincident 
with)  web  is  given  in  table  for  beams.  In  all  other  respects, 
proceed  for  this  form  of  section  as  in  the  previous  case. 

If  two  channels  are  connected  by  means  of  two  plates  instead 
of  a  beam,  as  shown  by  Fig.  2,  on  page  26,  the  moment  of  inertia 
of  the  plates  must  be  obtained  instead  of  the  beam.  This 
moment  'of  inertia,  for  a  neutral  axis  through  center  of  section 
perpendicular  to  the  plates,  is  equal  to  the  cube  of  the  width  of 
plate  multiplied,  by  T^th  of  the  thicknesses  of  the  two  plates 
added;  and  for  a  neutral  axis  parallel  to  plates,  is  equal  to  the 
area  of  the  two  plates  multiplied  by  the  square  of  the  distance 
between  the  center  of  the  plate  and  the  center  of  the  section. 

A  column  is  square  bearing  when  it  has  square  ends  which 
butt  against  or  are  firmly  connected  with  an  immovable  surface, 
such  as  the  floor  of  a  building;  it  is  pin  and  sqttare  bearing 
when  one  end  only  is  square  bearing  and  the  other  presses  against 
a  close  fitting  pin,  and  it  is  pin  bearing  when.both  ends  are  thus 
pin-jointed,  (for  example,  the  posts  in  pin-connected  bridges.) 

With  regard  to  the  table  on  the  Safe  Resistance  of  Wooden 
Pillars,  it  should  be  said  that  comprehensive  tests  establishing 
the  constants  to  be  used  in  the  formula  have  not  been  made  to 
date,  but  it  is  believed  that  the  values  given  in  table  err  on  the 
side  of  safety. 

EXAMPLES   OF   APPLICATION   OF   TABLES. 

I.  WThat  is  the  ultimate  strength  of  a  square  bearing  10" 
octagon  column,  ^"  thick  and  20'  long? 

Answer :  The  area  of  a  10"  X  YZ"  column,  as  per  table  on 
page  77,  is  21.3  square  inches.  The  mean  diameter  is  10",  very 

75 


1          20 
nearly,  so  that  ~-r-=  -v«    =  2,  for  which  the  ultimate  strength, 

as  per  table  on  page  79,  =  33560  Ibs.  per  square  inch.  Conse- 
quently the  ultimate  strength  of  the  column  •=  33560  Ibs.  X  21.3 
=  714800  Ibs.  The  safe  resistance  for  quiescent  loads  would  be 
=  X  X  714800  =  178700  Ibs.,  and  for  moving  loads  =  i  X 
714800  =  143000  Ibs. 

II.  Required   the   ultimate   strength  of  a  30  Ib.  10"  beam 
used  in  the  form  of  a  strut,  riveted  at  its  ends  so  as  to  be  firmly 
fixed,  and  measuring  10'  between  the  points  where  it  is  held  in 
position. 

By  reference  to  table  on  page  64,  the  least  radius  of  gyration 
of  a  30  Ib.   10"  beam  is  found   to   be  =  0.94,    (neutral   axis 

coincident  with  web,)  so  that  —  ==-_  g—  =  10.6,  for  which  the 

ultimate  strength,  as  per  table  on  page  80,  =27600  Ibs.  per  square 
inch.  The  area  of  the  beam  being  =±  9  square  inches,  its 
ultimate  strength  will,  therefore,  =  9  X  27600  =  248400  Ibs. 

III.  What  is  the  radius   of  gyration  of  a    column   section 
composed  of  two  9",  18  Ib.  channels,  and  a  6",  13>^  Ib.  beam, 
riveted  together  in  the  manner  shown  by  Fig.  3,  on  page  26  ? 

Answer,  if  neutral  axis  coincident  with  web  of  beam  : 
Moment  of  inertia  of  beam        ^=      2.0 
«       "   channels  =  129.6 

«         "    •     "       "  section     =  131.6 
•   Area  of  section  =  14.85  square  inches.    .Therefore  radius  of 


131.6 


gyration  =  ~\, 

Answer,  if  neutral  axis  at  right  angles  to  web  of  beam : 
Moment  of  inertia  of  beam  =  -         -     .    -       24.5. 

Moment  of  inertia  of  channels  =  area  of  channels  X 
distance  of  center  of  gravity  from  center  of  section 
squared  =  10.8  square  inches  X  3.68  =  -  -  146.3 

Moment  of  inertia  of  section  =          ....       170.8 

Therefore  radius  of  gyration  =  y/"TToc'  ==  3.39. 

^ 


vv                                                                                                  or 

3-  ~* 

KEYSTONE  OCTAGON  COLUMNS. 

Thicknesses  and  Corresponding  Areas  and  "Weights  per  Foot. 

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77 

ULTIMATE    STRENGTH 

OF 

HOLLOW     CYLINDRICAL     CAST     AND 

WROUGHT    IRON    COLUMNS, 

For  different  proportions  of  length  in  feet  (  =  1  ) 

To  least  diameter  in  inches  (=  d). 

Ultimate  Strength  in  Ibs.  per 

square  inch  = 

Cast    Iron. 

Wrought    Iron. 

Square  Bearing  :  Pin  &  Square  :  Pin  Bearing  : 

Square  Bearing  :    Pin  &  Square  :    Pin  Bearing  : 

80000         80000         80000 

40000          40000 

40000 

(121 

)2  1  ,  3(12  1)2        (1! 
I2      M600  d2      '40 

21)2 

(12  1)2           (12  1)2          (12  1)2 

"^800  ( 

Od2 

"^OOOd2       '20004^      '  1500  d2 

To  obtain  Safe 

Resistance  : 

For  quiescent  loads  (buildings)  divide  bjr{  J  f«  ^oughTiron. 

For  moving-  loads  (bridges)  divide  by       <  ?  r°r             £?'• 
'        (5  for  wrought  iron. 

Cast  Iron. 

"Wrought  Iron. 

1       Ultimate  Strength  in  Lbs.  per  sq.  in. 

Ultimate  Strength  in  Lbs.  per  sq.in. 

Square. 

Pin  and        p. 
Square.   ;      Pm' 

Square. 

Pin  and 
Square. 

Pin. 

1.0     '    67800 

62990        58820 

38170 

37310 

36500 

1.1         65690  - 

60300        55730 

37800 

36790 

35840 

1.2        63530 

57600 

52690 

37410 

36240 

35140 

1.3 

61340 

54930        49740 

37000 

35660 

34420 

1.4 

59140 

52310 

46900 

36560 

35050 

33670 

1.5 

56940 

49770 

44200 

36100 

34420 

32890 

1.6 

54760 

47300 

41630 

35620 

33770 

32110 

1.7 

52620 

44940 

39210 

35130 

33110 

31320 

1.8  ' 

50530 

42670 

36930 

34620 

32430 

30510 

1.9 

48490 

40510 

34790 

34090 

31750 

29710 

2.0 

48510 

38460 

32790 

33560 

31060 

28900 

2.1 

44600 

38520 

30920 

38010 

30360 

28100 

2.2 

42750 

34680 

29180 

32460 

29660 

27310 

2.3 

40980 

32940 

27540 

31900 

28970 

25530 

2.4        39280 

31310 

28030 

31340 

28270 

25760 

2.5     1    37650 

29770 

24620 

30770 

27590 

25000 

2.6    !    38090 

28320        23300 

30200 

26900 

24260 

2.7 

34600 

26950        22070 

29630 

26230 

23530 

2.8 

33180 

25670 

20930 

29060 

25570 

22820 

2.9 

31820 

24460 

19 

860 

28500 

24910 

22130 

3.0 

30530 

23320 

18870 

27930 

24270 

21460 

3.1 

29310 

22250    i    17940 

27370 

23640 

20810 

3.2 

28140 

21250        17070 

26820 

23020 

20170 

3.3 

27030 

20300    !    16260 

26270 

22420 

19560 

,    3.4        25970 

19410        15500 

25730 

21830 

18960  , 

79 

ULTIMATE   STRENGTH    OF  WROUGHT 
IRON    COLUMNS, 

For  different  proportions  of  length  in  feet  ( =  1 ) 
To  least  radius  of  gyration  in  inches  (=  r). 

Ultimate  Strength  in  Ibs.  per  square  inch  = 


Column 

Square  Bearing  : 
40000 


«    , 


(121)* 
36000  r2 


Column 

Pin  and  Square  Bearing 
40000 

(121)*." 
24000 r2  " 


Column 

Pin  Bearing  : 

40000 


14 


IJL 


18000  r2 


To  obtain  Safe  Resistance  : 

For  quiescent  loads,  as  in  buildings,  divide  by  4. 
For  moving  loads,  as  in  bridges,  divide  by  5. 

Ultimate  Strength  in  Lbs. 


Ultimate  Strength  in  Lbs. 
1  per  square  inch. 


3.0 
3.2 
3.4 
3.6 
3.8 

4.0 
4.2 
4.4 
4.6 
4.8 

5.0 
5.2 
5.4 
5.6 

5.8 

6.0 
6.2 
6.4 
6.6 
6.8 

7.0 
7.2 
7.4 
7.6 

7.8 


38610 
33430 
38230 
38030 
37820 

37590 
37360 
37120 
38870 
36620 

36360 
36090 
35820 
35540 
35260 

34970 
34870 
34370 
34060 
33750 

33440 
33130 
32810 
32490 
32170 


37950 
37680 
37400 
37110 
36810 

36500 
36170 
35840 
35500 
35140 

34780 
34420 
34050 
33670 
33280 

32890 
32500 
32110 
31710 
31310 

80910 
30510 
30110 
29710 
29310 


37310 
36970 
36610 
36240 
35860 

35460 
35050 
34640 
34210 
33770 

33330 
32890 
32440 
31980 
31520 

31060 
30590 
30130 
29670 
29200 

28740 
28270 
27820 
27360 
26910 


8.0 
8.2 
8.4 
8.6 

8.8 

9.0 
9.2 
9.4 
9.6 
9.8 

10.0 
10.2 
10.4 
10.6 
10.8 

11.0 
11.2 
11.4 
11.6 
11.8 

12.0 

12.2 
12.4 
12.6 
12.8 


per  square  inch. 


Square. 

Square!' 

Pin. 

31850 

28900 

26460 

31520 

28500 

26010 

31190 

28100 

25570 

30870 

27700 

25130 

30540  ; 

27310 

24700 

30210  : 

26920  : 

24270 

29880 

26530  ' 

23850 

29550 

26140 

23430 

29230  ; 

25760  i 

23030 

28900  ; 

25370  | 

22620 

28570  ! 

25000  ' 

22220 

28250  I 

24630 

21830 

27920  i 

24260 

21440 

27600  1 

23890 

21060 

27270  I 

23530 

20690 

26950 

23170 

20330 

26640 

22820 

19960 

26320 
26000 
25690 

25380 
25070 
24770 
24470 
24170 


22470 
22130 
21800 

21460 
21130 
20810 
20490 
20180 


19610 
19270 
18930 

18590 
18260 
17940 
17620 
17310 


80 


^ 

ULTIMATE   STRENGTH    OF 

RECTANGULAR  TIMBER  PILLARS,  WELL 

SEASONED, 

For  different  proportions  of  length  in  feet  (=  1) 

To  least 

diameter  or  side  in  inches  (=  d). 

Ultimate  Strength  in  Ibs.  per  square  inch  = 

Pillar 

Pillar                             Pillar 

Square  Bearing:        Pin  and  Square  Bearing  :           Pin  Bearing: 

5600 

5600                             5600 

(121)' 
"   550  d^ 

1.5(121)* 

1    ,     (121)2 

550  d^ 

275 

The  above  formula  for  Square  Bearing  Pillars  is  based  upon 

Lemande's  experiments  on  French  oak,  and  agrees  fairly  with 

Hodgkinson's 

formula 

for  French  oak  pillars  of  30  diameters 

and  over. 

The  strength  of  pillars  of  French  oak,  Red  deal  and  Dantzig 

oak,  is  given 

by  Hodgkinson  as  proportional  to  the  ratio,  6.9: 

7.8:  10.95. 

It  is  believed  the  above  formulae  for  French  oak  and  the  fol- 

lowing table  calculated 

from  them,  will  also  apply  to  American 

white 

pine  of  best  quality. 

Green  timber  has  only  about  half  the  strength  of  dry. 

To  obtain  the  Safe  Resistance,  divide  by  6. 

Ultimate  Strength 

in  Lbs. 

Ultimate  Strength  in  Lbs. 

1 

per  square  inch. 

1 

per  square  inch. 

T 

Square. 

Pin  and 
Square. 

Pin. 

d 

Square. 

Pin  and 
Square. 

Pin. 

1.0 

4440  - 

4020 

3680 

2.5 

2120 

1620 

1310 

1.1 

4250 

3800 

3430 

2.6 

2020 

1530 

1230 

1.2 

4070 

3580 

3190 

2.7 

1930 

1450 

1160 

1.3 

3880 

3370 

2970 

2.8 

1830 

1370 

1100 

1.4 

3700 

3160 

2760 

2.9 

1750 

1300 

1040 

1.5 

3520 

2970 

2570 

3.0 

1670 

1230 

980 

1.6 

3350 

2790 

2390 

3.1 

1590 

1170 

930 

1.7 

3190 

2620 

2230 

3.2 

1520 

1120 

880 

1.8 

3040 

2470 

2080 

3.3 

1450 

1060 

840 

1.9 

2890 

2320 

1940 

3.4 

1390 

1010 

790 

2.0 

2740 

2180 

1810 

3.5 

1330 

960 

760 

2.1 

2600 

2050 

1690 

3.6 

1270 

920 

720 

2.2 

2470 

1930 

1580 

3.7 

1220 

880 

690 

2.3 

2350 

1820 

1490 

3.8 

1170 

840 

650 

2.4 

2230 

1720 

1400 

3.9 

1120 

800         620 

81                                                    ™ 

GENERAL  NOTES  ON  FLOORS  and  ROOFS. 

On  page  23  will  be  found  examples  of  floor  joists  and  their 
connections.  When  two  beams  are  placed  side  by  side,  as  in 
Fig.  1,  they  should  be  connected  together  by  means  of  bolts  and 
cast-iron  separators,  fitted  closely  between  the  flanges  of  the 
beams.  The  office  of  these  separators  is  to  hold  in  position  the 
compression  flange  of  the  beams,  preventing  side  deflection  or 
buckling,  and  to  firmly  unite  the  two  beams,  so  that  they  will 
act  in  unison.  Separators  should  be  used  near  the  supports  and 
at  distances  of  five  or  six  feet.  They  are  shown  by  Figs.  2  and  3, 
on  page  24.  Their  weight  will  range  from  19  Ibs.  for  the  heavy 
15"  beams,  to  5  Ibs.  for  6"  beams. 

Figures  1,  2  and  3  show  the  methods  of  connecting  beams 
with  each  other.  In  Figs.  1  and  2  the  lighter  beam  is  coped 
into  the  heavier  one,  the  weight  being  carried  by  the  lower  flange 
of  the  latter.  The  angle  with  which  the  webs  are  connected, 
serves  only  to  hold  the  beams  in  position,  in  this  case.  In  Fig. 
3  the  load  of  the  smaller  beams  is  transferred  to  the  larger  by 
means  of  angles  riveted  to  the  webs,  and  in  case  this  is  not 
sufficient,  an  angle  may  be  riveted  to  the  web  of  the  larger 
'beam  underneath  the  smaller,  as  shown,  to  assist  in  carrying  the 
load. 

Figures  5,  6,  7,  8,  9  and  10,  on  page  23,  are  illustrations  of 
various  forms  of  girders,  such  as  it  is  often  necessary  to  use  in 
the  front  of  buildings,  to  carry  walls,  or  in  the  interior,  to  support 
the  joists.  Where  these  girders  rest  upon  the  wall,  cast  or  wrought- 
iron  bed  plates  should  be  used,  to  distribute  the  pressure  over  a 
greater  surface,  and  thereby  prevent  the  crushing  of  the  brick 
directly  under  the  girder.  In  some  cases  a  tough,  large  size 
stone  will  answer  without  the  plates,  but  where  the  pressure  is 
heavy,  both  plates  and  stone  should  be  used.  Figs.  5,  6,  9  and  10, 
are  illustrations. 

On  page  24,  Fig.  1,  is  represented  a  girder  composed  of  two 
beams,  carrying  a  brick  wall,  in  position.  In  case  of  failure  of  the 
girder,  only  a  part  of  the  wall  above  it  would  drop  down,  the 
line  of  rupture  for  brick-work  making  an  angle  of  about  30° 
with  the  vertical,  called  the  angle  of  repose.  The  weight  to  be 

82  " 


carried  by  the  girder  may,  therefore,  be  considered  to  be  only  that 
part  of  the  wall  between  the  lines  of  rupture,  provided,  that  in 
building  the  wall,  the  center  of  the  girder  was  supported  tem- 
porarily with  a  wooden  prop,  preventing  deflection.  Several 
courses  should,  however,  be  laid  before  this  is  done. 

If  /=  the  clear  span  of  girder,  and  h  =  the  hight  of  wall 
above  it,  the  superficial  area  of  the  trapezoid  between  the  lines 
of  rupture,  is  expressed  by  h  (2  1  —  1.2  h),  but  deductions  must, 
of  course,  be  made  for  windows  or  other  openings  in  the  wall, 
if  there  are  any. 

In  order  to  be  entirely  on  the  safe  side,  and  also  for  the  sake 
of  simplicity,  the  weight  of  wall  between  vertical  lines  directly 
over  the  girder,  is  frequently  adopted  as  the  load  to  be  carried 
by  it. 

Weight  of  Brick-ivork  per  Superficial  Foot,  for  a 
9"  wall  =  84  Ibs.,  13"  wall  =  121  Ibs.,  18"  wall  =  168  Ibs., 
one  cubic  foot  weighing  112  Ibs. 

There  are  various  fire-proof  floors  in  use;  one  of  the  most 
common  is  that  represented  by  Fig.  1,  on  page  23.  Four-inch 
brick  arches  are  built  between  beams  spaced  not  over  5  feet  apart, 
and  tied  together  by  rods  %"  to  1"  diameter,  at  intervals  of  4' 
to  6',  so  as  to  take  the  thrust  of  the  arches  off  the  walls.  Tee  or 
angle  irons  are  inserted  in  the  wall,  so  as  to  hold  it  firmly  in  line 
between  the  points  held  by  the  rods.  The  top  of  the  arches  is 
leveled  off  with  concrete,  allowing  space,  however,  for  wooden 
strips,  to  which  the  floor  timber  is  nailed.  The  plastering  for 
ceiling  usually  covers  the  arches  only,  so  that  the  ceiling  will 
appear  curved  and  show  the  lower  flanges  of  the  iron  beams. 

A  convenient  device  for  centering  the  arches  is  shown  in 
Fig.  4.  The  centers  are  suspended  by  iron  hooks  from  the  lower 
flanges  of  the  beams,  and  can  be  moved  forward  and  back,  and 
removed  at  pleasure. 

Figure  4,  on  page  24,  and  Fig.  3,  on  page  25,  are  examples  of 
flush,  plastered  ceilings,  the  laths  in  the  latter  case  being  held  by 
light  castings.  Fig.  3,  on  page  24,  is  an  example  of  an  iron 
ceiling,  composed  of  sheet  iron  pressed  to  suitable  form,  laid 
upon  the  lower  flanges  of  the  beams;  .  and  Figs.  2  and  5  are 
_ 


illustrations  of  corrugated  iron  ceilings.  Both  are  open  to  the 
objection  that  the  condensed  moisture  of  the  air  will  collect 
upon  the  iron  and  fall  into  the  rooms  below.  Particularly  is  this 
the  case  in  rooms  filled  with  people,  and  such  ceilings  should, 
therefore,  be  restricted  in  their  use,  or  the  iron  should  be  covered 
in  such  manner  from  below,  that  the  access  of  the  air  is  effectually 
cut  off,  as  by  plastering. 

The  weight  of  a  fire-proof  floor,  consisting  of  four-inch  brick 
arches  between  beams,  with  concrete  filling  above  the  arches  and 
flooring,  will  generally  average  about  70  Ibs.  per  square  foot, 
exclusive  of  the  weight  of  the  beams.  The  following  are  average 
weights  of  some  other  constructions,  and  the  usual  assumptions 
made  for  superimposed  load: 

Iron  roof  of  100  feet  span,  with  corrugated  iron  laid  directly 
upon  purlins,  will  weigh 

Approximately,      -         -         -         -         -         -    -10  Ibs.  ^  sq.  ft. 

If  boarded,  add 3  " 

For  lathed  and  plastered  ceiling,  allow    -         -     10       "  " 
For  snow  and  vertical  component  of  wind  force, 

allow 30 

For  superimposed  load  on 

Floors  of  dwellings,  assume       -         -         -     60  "  " 

"      "    churches,  theaters  and  ball  rooms,  125  "  " 

"      "    warehouses,        -                                  250  "  " 

Weight  of  snow,  freshly  fallen,  -         -  5  to  12  "    cub.  ft. 

"               "      saturated,  (slush,)          -               40  "  " 

Crowd  of  people,  closely  packed,         -                    80  "  sq.  ft. 

Wind  pressure  (violent  hurricane,)           -                50  "  " 

Rule  for  finding  the  sectional  area  of  a  bar  of  wrought  iron, 
given  the  weight  per  foot : 

Multiply  by  3  and  divide  by  10. 

Rule  for  finding  the  weight  per  foot,  given  the  area  : 

Divide  by  3  and  multiply  by  10. 

84  ® 


CORRUGATED  AND  GALVANIZED  IRON. 

Corrugated  Iron  is  used  for  roofs  and  sides  of  buildings.  It  is 
usually  laid  directly  upon  the  purlins  in  roofs,  and  held  in  place  by 
means  of  clips  of  hoop  iron,  which  encircle  the  purlin  and  are 
placed  in  distances  of  about  twelve  inches  apart.  Special  care 
must  be  taken  that  the  projecting  edges  of  the  corrugated  iron, 
at  the  -eaves  and  gable  ends,  of  the  roof,  are  well  secured,  other- 
wise the  wind  will  loosen  the  sheets  and  fold  them  up. 

The  corrugations  are  made  of  various  sizes ;  the  smaller 
present  a  more  pleasing  appearance  to  the  eye,  while  the  larger 
are  stiffer  and  will  span  a  greater  distance,  thereby  permitting  the 
purlins  to  be  placed  further  apart.  The  sizes  of  sheets  generally 
used  for  both  roofing  and  siding,  are  No.  20  and  22. 

The  corrugated  iron  which  will  be  described  in  the  following, 
is  manufactured  by  the  Keystone  Bridge  Company,  of  Pittsburgh. 
It  is  of  medium  size,  presenting  both  a  good  appearance  and 
being  of  sufficient  strength  for  usual  requirements. 

By  one  corrugation  is  meant  the  double  curve  between  corre- 
sponding points,  and  by  depth  of  corrugation,  the  greatest  deviation 
from  the  straight  line,  measured  between  the  concave  surfaces  of 
the  corrugated  sheet. 

The  Keystone  Bridge  Company's  corrugations  are  2.425"  long, 
measured  on  the  straight  line ;  they  require  a  length  of  iron  of 
2.725/;  to  make  one  corrugation,  and  the  depth  of  corrugation 
is  |4".  One  corrugation  is  allowed  for  lap  in  the  width  of  the 
sheet  and  ft"  in  the  length,  for  the  usual  pitch  of  roof  of  two  to 
one.  Sheets  can  be  corrugated  of  any  length  not  exceeding 
ten  feet.  The  most  advantageous  width  is  30^ /;,  which 
(allowing  y2"  for  irregularities)  will  make  eleven  corrugations 
=  30",  or,  making  allowance  for  laps,  will  cover  24^"  of  the 
surface  of  the  roof. 

By  actual  trial  it  was  found  that  corrugated  iron  No.  20, 
spanning  6  feet,  will  begin  to  give  a  permanent  deflection  for  a 
load  of  30  Ibs.  per  square  foot,  and  that  it  will  collapse  with  a 
load  of  60  Ibs.  per  square  foot.  The  distance  between  centers 
of -purlins  should  therefore  not  exceed  6  feet,  and,  preferably, 
be  less  than  this. 


£— 

KEYSTONE  BRIDGE   CO.'S   CORRUGATED 

IRON. 

The  following  table  is  calculated  for  sheets  3C 

y^11  wide  before 

corrugating. 

I       J^ 

Weight  per  Square  of  100  square 

feet, 

|| 

when 

laid,  allowing  6"  lap  in  length  and 
or  one  corrugation  in  width    of 

.O.SJf           JSJ3           Jjp2        jjjf'l 

she4et 

for  sheet  lengths  of: 

'Ijf3 

Lbs.        Lbs. 

5' 

6' 

7'      8' 

9' 

10' 

« 

LbT 

16       .065    2.61     3.28 

365 

358 

353     350 

348 

346 

2.95 

18       .049     1.97     2.48 

275 

270 

267    264 

262 

261 

2.31 

20       .035     1.40     1.76 

196 

192 

190    188 

186 

185 

1.74 

22       .028     1.12     1.41 

156 

154 

152     150 

149 

148 

1.46 

24       .022      .88     1.11 

123 

121 

119     118 

117 

117 

1.22 

26       .018      .72       .91 

101 

99 

97      97 

96 

95 

1.06 

RESULTS  OF  TEST 

of  a  corrugated  sheet  No.  20, 

2/_0"  wide,  6'-0"  long  between 

supports,  loaded  uniformly  with  fire  clay. 

Load 
per  Square  Foot. 
Lbs. 

Deflection 
at  Center  under  Load. 
Inches. 

Permanent  Deflection, 
Load  Removed. 

5 

/2 

0 

10 

X 

0 

15 

1 

0 

20 

1 

0 

25 

1 

0 

30 

] 

H 

% 

35 

2 

Vt 

Yz 

40 

2 

1  /o 

K' 

45 

3/2 

] 

-/& 

50 

4 

] 

•Y* 

55 

C 

# 

Not 

Noted. 

60 

Broke 

Down. 

" 

a 

86 

ILLUSTRATION     OF    APPLICATION 

OP    TABLES    ON    FLAT    ROLLED    IRON. 

Pages  88  to  99,  inclusive. 

What  is  .the  weight  per  foot  of  a  bar  5"  X  IjV'  in  section? 
Answer  :  In  the  column  for  5"  width,  and  in  the  line  for  1  j1^" 
thickness,  will  be  found  the  value  17.71,  which  is  the  weight 
desired. 

What  thickness  of  4^"  bar  will  be  required  to  give  an  area 
of  5.3  square  inches?  Answer:  In  the  column  for  4^"  width 
will  be  found  5.34,  which  is  the  area  nearest  to  that  required ; 
the  corresponding  thickness  being  IfV '»  tne  ^ar  should  be  4^" 
X  W- 


ILLUSTRATION     OF    APPLICATION 

OP    TABLES    ON    DECIMAL    PARTS    OP    A 
FOOT  FOR  EACH       th  OP  AN  INCH. 


Pages  1OO  to  1O3,  inclusive. 

What  is  the  value  of  5'  —  7^  \"  ,  expressed  in  feet  and  decimals 
of  a  foot?  Answer  :  5.5977;  found  by  looking  in  column  for  7", 
and  in  line  for  \\". 

What  is  the  value  of  11.6838',  expressed  in  feet,  inches  and 
fractions  of  an  inch?  Answer:  The  value  nearest  to  the 
decimal  .6833,  to  be  found  in  table,  is  .6836,  which  is  =  8$f  ", 
therefore  11.6838'  =  11'  —  8JJ",  nearly. 


87 


WEIGHTS    OF    FLAT    ROLLED   IRON 

PER    LINEAL    FOOT. 

For  Thicknesses  from  -y^  in.  to  2  in.  and  Widths 

from  1  in.  to  12%  In. 

Iron  weighing  480  Ibs.  per  cubic  foot. 

Thickness 
in  Inches. 

1" 

i  //] 

IK" 

2" 

2)i" 

2K" 

2fc" 

12" 

* 

.208 

.260      .313 

.365 

.417 

.469     .521 

.573 

2.50 

.417 

.521      .625    .729 

.833 

.938  1.04  . 

1:15 

5.00 

A 

.625 

.781      .938 

1.09 

1.25 

1.41 

1.56 

1.72 

7.50 

i 

.833 

1.04 

1.25 

1.46 

1.67 

1.88 

2.08 

2.29 

10.00 

TS 

1.04 

1.30 

1.56 

1.82 

2.08 

2.34 

2.60 

2.86 

12.50 

f 

1.25 

1.56 

1.88 

2.19 

2.50 

2.81 

3.13 

3.44 

15.00 

A 

1.46 

1.82- 

2.19 

2.55 

2.92 

3.28 

3.65 

4.01 

17.50 

I 

1.67 

2.08 

2.50 

2.92    3.33 

3.75 

4.17 

4.58 

20.00 

j\ 

1.88 

2.34 

2.81 

3.28 

3.75 

4.22 

4.69 

5.16 

22.50 

1 

2.08 

2.60 

3.13 

3.65 

4.17 

4.69 

5.21 

5.73 

25.00 

e 

2.29 

2.86 

3.44 

4.01 

4.58 

5.16 

5.73 

6.30 

27.50 

2.50 

3.13 

3.75 

4.38 

5.00 

5.63 

6.25 

6.88 

30.00 

it 

2.71 

3.39   !  4.06 

4.74 

5.42 

6.09 

6.77 

7.45 

32.50 

2.92 

3.65     4.38 

5.10 

5.83 

6.56 

7.29 

8.02 

35.00 

it 

3.13 

3.91     4.69 

5.47 

6.25 

'7.03 

7.81 

8.59 

37.50 

1 

3.33 

4.17     5.00 

5.83 

6.67 

7.50 

8.33 

9.17 

40.00 

i-V 

3.54 

4.43     5.31 

6.20    7.08 

7.97 

8.85 

9.74 

42.50 

li- 

3.75 

4.69 

5.63 

6.56    7.50 

8.44 

9.38 

10.31 

45.00 

ly3^ 

3.96 

4.95 

5.94 

6.93  I  7.92 

8.91 

9.90 

10.89 

47.50 

H 

4.17 

5.21 

6.25 

7.29    8.33 

9.38 

10.42 

11.46 

50.00 

IA 

4.37 

5.47  i  6.56 

7.66  1  8.75 

9.84 

10.94 

12.03 

52.50 

4.58 

5.73     6.88 

8.02    9.17 

10.31   11.46 

12.60 

55.00 

IJZg. 

4.79 

5.99 

7.19 

8.39    9.58  10.78  11.98 

13.18 

57.50 

11 

5.00 

6.25 

7.50 

8.75  10.00 

11.25 

12.50 

13.75 

60.00 

1T9^ 

5.21 

6.51     7.81 

9.11  !10.42 

11.72 

13.02 

14.32 

62.50 

If 

5.42 

6.77     8.13 

9.48  10.83 

12.19 

13.54 

14.90 

65.00 

ift 

5.63 

7.03     8.44 

9.84  111.25 

12.66 

14.06 

15.47 

67.50 

If 

5.83 

7.29 

8.75 

10.21  111.67 

13.13 

14.58 

16.04 

70.00 

113 

6.04 

7.55 

9.06 

10.57  12.08 

13.59 

15.10 

16.61 

72.50 

1? 

6.25 

7.81 

9.38 

10.94 

12.50  (14.06 

15.63 

17.19 

75.00 

6.46 

8.07     9.69 

11.30 

12.92  14.53 

16.15 

17.76 

77.50 

2 

6.67 

8.33    10.00 

11.67 

13.33  15.00 

16.67 

18.33 

80.00 

'4 

j 

i 

WEIGHTS   OF  FLAT  ROLLED  IRON 

PER  LINEAL  FOOT. 

(CONTINUED.) 

Thickness 
in  Inches. 

3" 

3K" 

3^" 

g3///    4// 

4H» 

4K" 

12" 

625 

.677 

.729 

.781 

.833 

.885 

.938 

.990 

2.50 

? 

1.25 

1.35 

1.46 

1.56 

1.67 

1.77 

1.88 

1.98 

5.00 

A 

1.88 

2.03 

2.19 

2.34 

2.50 

2.66 

2.81 

2.97 

7.50 

i 

2.50 

2.71 

2.92 

3.13 

3.33 

3.54 

3.75 

3.96 

10.00 

_5_ 

3.13 

3.39 

3.65 

3.91 

4.17 

4.43 

4.69 

4.95 

12.50 

3. 

3.75 

4.06 

4.38 

4.69 

5.00 

5.31 

5.63 

5.94 

15.00 

^ 

4.38 

4.74 

5.10 

5.47 

5.83 

6.20 

6.56 

6.93 

17.50 

\6       5.00 

5.42 

5.83 

6.25 

6.67 

7.08 

7.50 

7.92 

20.00 

•Ar     I  5.63 

6.09 

6.56 

7.03 

7.50 

7.97 

8.44 

8.91 

22.50 

f 

6.25 

6.77 

7.29 

7.81 

8.33 

8.85 

9.38 

9.90 

25.00 

H 

6.88 

7.45 

8.02 

8.59 

9.17 

9.74 

10.31 

10.89 

27.50 

7.50 

8.13 

8.75 

9.38  110.00 

10.63 

11.25 

11.88 

30.00 

it 

8.13    8.80 

9.48 

10.16 

10.83 

11.51 

12.19 

12.86 

32.50 

1 

8.75 

9.48 

10.21 

10.94 

11.67 

12.40 

13.13 

13.85 

35.00 

It 

9.38 

10.16 

10.94 

11.72 

12.50 

13.28 

14.06 

14.84 

37.50 

1 

10.00 

10.83  11.67 

12.50 

13.33 

14.17 

15.00 

15.83 

40.00 

JTC 

10.63 

11.51  12.40 

13.28 

14.17 

15.05 

15.94 

16.82 

42.50 

l1! 

11.25 

12.19  13.13 

14.06 

15.00 

15.94 

16.88 

17.81 

45.00 

11.88 

12.86  13.85 

14.84 

15.83 

16.82 

17.81 

18.80 

47.50 

H 

12.50 

13.54  14.58 

15.63 

16.67 

17.71 

18.75 

19.79 

50.00 

i 

JL 

13.13 

14.22  15.31 

16.41 

17.50 

18.59 

19.69 

20.78 

52.50 

f      13.75  14.90  16.04 

17.19 

18.33 

19.48 

20.63 

21.77 

55.00 

TV     .14.38  15.57  16.77 

17.97 

19.17 

20.36  21.56 

22.76 

57.50 

.V      15.00 

16.25  17.50 

18.75 

20.00 

21.25 

22.50 

23.75 

60.00 

A     15.63 

16.93  18.23 

19.53 

20.83 

22.14 

23.44 

24.74 

'62.50 

4       16,25  17.60  18.96 

20.31 

21.67  23.02 

24.38 

25.73 

65.00 

m     16,88  18.28  19.69 

21.09 

22.50  123.91 

25.31 

26.72 

67.50 

1  f       17.50 

18.96  20.42 

21.88 

23.33  J24.79 

26.25 

27.71 

70.00 

Hf      18.13  19.64  21.15  |22.66 

24.17  25.68  27.19  28.70 

72.50 

1  1       18.75  '20.31  21.88  23.44 

25.00  26.56  i28.13  29.69 

75.00 

U|     19.38  ;20.99  22.60 

24.22 

25.83  27.45  J29.06 

30.68 

77.50    • 

2          20.00  21.67  23.33 

25.00 

26.£7  28.33  !30.00  31.67 

80.00 

WEIGHTS   OP  FLAT  ROLLED   IRON 
PER  LINEAL  FOOT. 

(CONTINUED.) 


Thickness 
in  Inches. 

5" 

6«» 

m» 

5K" 

6" 

6*»  6X» 

6X» 

12" 

Te" 

1.04 

1.09 

1.15     1.20 

1.25 

1.30  i   1.35 

1.41 

2.50 

2.08 

2.19 

2.29J  2.40 

2.50 

2.60 

2.71 

2.81 

5.00 

A 

3.13 

3.28 

3.44     3.59 

3.75 

3.91     4.06 

4.22 

7.50 

V 

4.17 

4.38 

4.58 

4.79 

5.00 

5.21     5.42 

5.63 

10.00 

T56 

5.21 

5.47 

5.73 

5.99 

6.25 

6.51     6.77 

7.03 

12.50 

6.25 

6.56 

6.88 

7.19 

7.50 

7.81     8.13 

8.44 

15.00 

ft 

7.29 

7.66 

8.02 

8.39 

8.75 

9.11     9.48 

9.84 

17.50 

i 

8.33 

8.75 

9.17 

9.58 

10.00 

10.42 

10.83 

11.25 

20.00 

T9* 

9.38 

9.84 

10.31 

10.78 

11.25 

11.72 

12.19 

12.63 

22.50 

5. 

10.42 

10.94   11.46 

11.98   12.50 

13.02 

13.54 

14.06 

25.00 

ft 

11.46 

12.03   12.60  '13.18   13.75 

14.32   14.90 

15.47 

27.50 

3 
4 

12.50 

13.13 

13.75 

14.38 

15.00 

15.63   16.25 

16.88 

30.00 

M 

13.54 

14.22 

14.90 

15.57 

16.25 

16.93  17.60 

18.28 

32.50 

14.58 

15.31 

16.04 

16.77  17.50 

18.23  18.96 

19.69 

35.00 

it 

15.63 

16.41 

17.19   17.97  18.75   19.53  j  20.31 

21.09 

37.50 

1 

16.67 

17.50 

18.33:19.17  20.00  20.83 

21.67 

22.50 

40.00 

!TV 

17.71 

18.59 

19.48  '  20.33  21.25  22.14 

23.02 

23.91 

42.50 

1| 

18.75 

19.69  20.63  jgl.56  22.50  j  23.44 

24.38 

25.31 

45.00 

19.79 

20.78 

21.77  1  22.76  23.75 

24.74 

25.73  1  26.72 

47.50 

1? 

20.83 

21.88 

22.92123.96  £5.00 

26.04 

27.08 

28.13 

50.00 

IJL 

21.88 

22.97 

24.03  25.1  6  !  26.25 

27.34  28.44 

29.53 

52.50 

If 

22.92 

24.06 

25.21 

26.35  ;  27.50 

28.65  29.79 

30.94 

55.00 

4 

23.96 

25.16 

26.35  27.55  28.75  29.95  31.15 

32.34 

57.50 

U 

25.00 

26.25 

27.50  28.75  30.00 

31.25  32.50 

33.75 

60.00 

1T^ 

26.04 

27.34 

28.65 

29.95  31.25 

32.55 

33.85 

35.16 

62.50 

H 

27.08 

28.44 

29.79   31.15   32.50 

33.85 

35.21 

86.56 

65.00 

m 

28.13 

29.53 

30.94  :  32.34  33.75 

35.16  :  36.56 

37.97 

67.50 

if 

29.17 

•30.63  i  32.08   33.54   35.00 

36.43  37.92 

39.38 

70.00 

Ht 

30.21 

31.72 

33.23   84.74 

36.25 

37.73 

39.27 

40.78 

72.50 

i? 

31.25 

32.81   34.38  35.94   37.50 

39.08  40.63 

42.19 

75.00 

lit 

32.29 

33.91 

35.52  37.14   38.75 

40.36  41.  98!  43.59 

77.50 

2 
i  

33.33 

35.00 

36.67  38.33 

40.00 

41.67 

43.33 

45.00 

80.00 

WEIGHTS   OF   FLAT   ROLLED  IRON 
PER  LINEAL  FOOT. 

.  (CONTINUED.) 

Thickness 
in  Inches. 

1" 

7M" 

7lo"  7%" 

8" 

«» 

8X»  W 

12" 

T6 

1.46 

1.51 

1.56;     1.61 

1.67 

1.72 

1.77 

1.82 

2.50 

2.92 

3.02 

3.13;   3.23 

3:33 

3.44 

3.54 

3.65 

5.00 

A 

4.38 

4.53 

4.69 

4.84 

5.00 

5.16 

5.31 

5.47 

7.50 

f* 

5.83 

6.04 

6.25 

6.46 

6.67 

6.88 

7.08 

7.29 

10.00 

jV 

7.29 

7.55 

7.81 

8.07 

8.33 

8.59 

8.85 

9.11 

12.50 

8.75 

9.06 

9.38!   9.69 

10.00 

10.31 

10.63 

10.94 

15.00 

i 

10.21 

10.57  i  10.94   11.30 

11.67 

12.03 

12.40 

12.76 

17.50 

i 

11.67 

12.08 

12.50   12.92 

13.33 

13.75 

14.17 

14.58 

20.00 

Kl 

13.13 

13.59 

14.06 

14.53 

15.00 

15.47 

15.94 

16.41 

22.50 

V 

14.58 

15.10 

15.63 

16.15   16.67 

17.19 

17.71 

18.23 

25.00 

A 

16.04 

16.61 

17.19 

17.76 

18.33 

18.91   19.48 

20.05 

27.50 

i 

17.50 

18.13 

18.75 

19.38 

20.00  i  20.63 

21.25 

21.88 

30.00 

It 

18.96 

19.64 

20.31 

20.99 

21.67 

22.34 

23.02 

23.70 

32.50 

7 

20.42  21.15 

21.88 

22.60 

23.33  24.06 

24.79 

25.52 

35.00 

ff      21.88 

22.66 

23.44  24.22   25.00  25.78 

26.56 

27.34 

37.50 

i 

23.33  24.17  25.00 

25.83  26.67  27.50 

28.33 

29.17 

40.00 

IT* 

24.79  25.68  26.56^7.45 

28.33  29.22 

30.10 

30.99 

42.50 

1? 

26.25 

27.19  28.13  29.06 

30.00  30.94 

31.88 

32.81 

45.00 

27.71 

28.70  i  29.69  30.68 

31.67  32.66 

33.65 

34.64 

47.50 

H 

29.17 

30.21  i  31.25 

32.29 

33.38  34.38 

35.42 

36.46 

50.00 

IA 

30.62 

31.72 

32.81 

33.91 

35.00 

36.09 

37.19 

38.28 

52.50 

1  -^ 

32.08 

33.23 

34.38 

35.52 

3C.67  1  37.81 

38.96 

40.10 

55.00 

l-7r 

33.54 

34.74 

35.94   37.14   38.33   39.53 

40.73 

41  93 

57.50 

H 

35.00 

36.25 

37.50 

38.75 

40.00 

41.25 

42.50 

4^.75 

^A.00 

JJL 

36.46  !  37.76 

39.06 

40.36 

41.67 

42.97 

44.27 

45.57 

62.50 

i.f 

37.92  39.27  40.63  41.98 

43.33   44.69  146.04 

47.40 

65.00 

39.38  '40.78  42,19 

43.59  '  45.00 

46.41 

47.81 

49.22 

67.50 

If"     140.83  42.29 

43.75 

45.21 

46.67 

48.13 

49.58 

51.04 

70.00 

lif 

42.29   43.80 

45.31 

46.82 

48.33 

49.84 

51.35 

52.86 

72.50 

1  i 

43.75!  45.31   46.88 

48.44   50.00 

51.56 

53.13 

54.69 

75.00 

HI 

45.21  I  46.82  i  48.44 

50.05  •  51.67 

53.28 

54.90 

56.51 

77.50 

2 

46.67 

48.33  !  50.00 

51.67  i  53.33 

55.00 

56.67 

53.33 

80.00 

3  — 

—~Ti 

WEIGHTS   OP  PLAT   ROLLED   IRON 

PEK  LINEAL  FOOT. 

(CONTINUED.) 

Thickness 
in  Inches. 

9"   \9%" 

&A" 

9%" 

10" 

1<H" 

10*" 

10f" 

12" 

rV 

1.88 

1.93 

1.98 

2.03 

2.08 

2.14 

2.19 

2.24 

2.50 

| 

3.75 

3.85 

3.96 

4.06 

4.17 

4.27 

4.38 

4.48 

5.00 

A 

5.63 

5.78 

5.94 

6.09 

6.25 

6.41 

6.56 

6.72 

7.50 

i 

7.50 

7.71     7.92    8.13 

o  oo 
o.oo 

8.54 

8.75 

8.96  < 

»10.00 

A 

9.38 

9.64 

9.90 

10.16 

10.42 

10.68 

10.94 

11.20 

12.50 

1 

11.25 

11.56 

11.88 

12.19 

12.50 

12.81 

13.13 

13.44 

15.00 

A 

13.13 

13.49 

13.85 

14.22 

14.58 

14.95 

15.31 

15.68 

17.50 

f 

15.00 

15.42 

15.83 

16.25 

16.67 

17.08 

17.50 

17.92 

20.00 

T96 

16.88 

17.34 

17.81 

18.28 

18.75 

19.22 

19.69 

20.16 

22.50 

1 

18.75 

19.27 

19.79 

20.31 

20.83 

21.35 

21.88 

22.40 

25.00 

e 

20.63 

21.20 

21.77 

22.34 

22.92 

23.49 

24.06 

24.64' 

27.50 

i 

22.50 

23.13 

23.75 

24.38 

25.00 

25.62 

26.25 

26.88 

30.00 

it 

24.38 

25.05 

25.73 

26.41 

27.08 

27.76 

28.44 

29.11 

32.50 

i 

26.25 

26.98 

27.71 

28.44 

29.17 

29.90 

30.63 

31.35 

35.00 

it 

28.13 

28.91 

29.69 

30.47 

31.25  1  32.03 

32.81 

33.59 

37.50 

i 

30.00 

30.83 

31.67 

32.50 

33.33 

34.17 

35.00 

35.83 

40.00 

i_i_ 

31.88 

32.76 

33.65 

34.53 

35.42 

36.30 

37.19 

38.07 

42.50 

i  - 

33.75 

34.69 

35.63 

36.56 

37.50 

38.44 

39.38 

40.31 

45.00 

l~V 

35.63 

36.61 

37.60 

38.59 

39.58 

40.57 

41.56 

42.55 

47.50' 

H 

37.50 

38.54 

39.58 

40.63 

41.67 

42.71 

43.75 

44.79 

50.00 

ifV 

39.38 

40.47 

41.56 

42.66 

43.75 

44.84  1  45.94 

47.03 

52.50 

H 

41.25 

42.40 

43.54 

44.69 

45.83 

46.98  !  48.13 

49.27 

55.00 

IA 

43.13 

44.32 

45.52 

46.72 

47.92 

49.11 

50.31 

51.51 

57.50 

H 

45.00 

46.25 

47.50 

48.75 

50.00  51.25 

52.50 

53.75 

60.00 

1T96 

46.88 

48.18 

49.48 

50.78 

52.08 

53.39 

54.69 

55.99 

62.50 

If 

48.75 

50.10 

51.46 

52.81 

54.17 

55.52 

56.88 

58.23 

65.00 

IH 

50.63 

52.03 

53.44 

54.84 

56.25 

57.66 

59.06 

60.47 

67.50 

11 

52.50 

53.96 

55.42  56.88 

58.33 

59.79 

61.25    62.71 

70.00 

HI 

54.38 

55.89  57.40  58.91 

60.42 

61.93 

63.44 

64.95 

72,50 

11 

56.25 

57.81   59.38  60.94 

62.50 

64.06 

65.63 

67.19 

75.00 

HI 

58.13 

59.74  61.35   62.97 

64.58 

66.20 

67.81 

69.43 

77.50 

2 

60.00 

61.67   63.33 

65.00 

66.67 

68.33 

70.00 

71.67 

80.00 

4  

• 

i 

WEIGHTS   OF  FLAT  ROLLED   IRON 

PER  LINEAL  FOOT. 

(CONTINUED.) 

Thickness 
in  Inches. 

11"   11±"'11$"  llf  12" 

12|" 

12$" 

12f" 

11 

I             ,             •             1             i 

A  * 

TV       2.29     2.34     2.40 

2.45 

2.50 

2.55 

2.60 

2.66 

p^  Ne0 

.3  X 

i     :  4.58     4.69     4.79 

4.90 

5.00 

5.10 

5.21 

5.31 

r^  ^ 

-A       6.88:  7.03^   7.19 

7.34 

7.50 

7.66 

7.81 

7.97 

CO 

i        9.17'    9.38     9.58 

9.79 

10.00 

10.21 

10.42 

10.63 

a 

TV      11.46  11.72   11.98 

12.24 

12.50 

12.76 

13.02 

13.28 

1! 

V      13.75   14.08   14.38 

14.69 

15.00 

15.31 

15.63 

15.94 

J  | 

TV      16.04   16.41    16.77 

17.14 

17.50 

17.86 

18.23 

18.59 

>-,_» 

i       18.33   18.75   19.17 

19.58 

20.00 

20.42 

20.83 

21.25 

|.g 

A      20.63  !  21.09  '  21.56 

22.03 

22.50 

22.97 

23.44 

23.91 

|| 

f       22.92 

23.44  23.96 

24.48 

25.00 

25.52 

26.04 

26.58 

•-§  "^ 

4-1    125.21   25.78!  26.35 

26.93 

27.50 

28.07 

28.65 

29.22 

i|  J 

I     127.50  28.13 

28.75 

29.38 

30.00 

30.63 

31.25 

31.88 

j 

».* 

i* 

29.79  30.47  31.15 

31.82 

32.50 

33.18 

33.85 

34.53 

•** 

1 

32.08  32.81  i  33.54 

34.27 

35.00 

35.73 

36.46 

37.19 

I  J 

44      34.38   35.18  35.94 

36.72 

37.50 

38.28 

39.06 

39.84 

3s 

1   '      38.67  ;  37.50  |  38.33 

39.17 

40.00 

40.83 

41.67 

42.50 

|-s 

|V 

38.96  39.84 

40.73 

41.61 

42.50 

43.39 

44.27 

45.16 

|x 

1? 

41.25 

42.19 

43.13 

44.06 

45.00 

45.94 

46.88 

47.81 

I3* 

•  Ij3r 

43.54 

44.53 

45.52 

46.51 

47.50 

48.49 

49.48 

50.47 

^\? 

1  1. 

45.83 

46.88 

47.92 

48.96 

50.00 

51.04 

52.08 

53.13 

Sis 

g^ 

1T5- 

48.13 

49.22 

50.31 

51.41 

52.50 

53.59 

54.69 

55.78 

tiu 

If 

50.42 

51.56  i  52.71 

53.85 

55.00 

56.15 

57.29 

58.44 

H 

52.71 

53.91  1  55.10 

56.30 

57.50 

58.70 

59.90 

61.09 

So5? 

1? 

55.00 

56.25 

57.50 

58.75 

60'.00 

61.25 

62.50 

63.75 

38 

1  9 

57.29 

58.59 

59.90 

61.20 

62.50 

63.80 

65.10 

66.41 

IsS 

H 

59.58 

60.94 

62.29 

63.65 

65.00 

66.35 

67.71 

69.06 

^  g-« 

61.88 

63.28 

64.69 

66.09 

67.50 

68.91 

70.31 

71.72 

"£  &  + 

if 

64.17 

65.63 

67.08 

68.54 

70.00 

71.46 

72.92 

74.38 

«S     f  oo 

Ht 

66.46 

67.97 

69.48 

70.99 

72.50 

74.01 

75.52 

77.03 

f  rt    B 

if 

68.75 

70.31 

71.88 

73.44 

75.00 

76.56 

78.13 

79.69 

jgJS 

lit 

,71.04 

72.66 

74.27 

75.89 

77.50 

79.11 

80.73 

82.34 

*"  M  x 

2 

73.33 

75.00 

76.67 

78.33 

80.00 

81.67 

83.33 

85.00 

'^  ~ 

f 

93                                                  0 

1  — 

a 

AREAS   OP  PLAT   ROLLED  IRON, 

For  Thicknesses  from  T^  in.  to  2  in.  and  Widths 

from  1  in.  to  12%  in. 

Thickness 

2K"  2K" 

in  Inches. 

~\."      l/^;/   IV"   \yn     2" 

2^ 

12" 

TV 

.063     .078     .094     .109 

.125     .141 

.156 

.172 

.750 

f 

.125 

.156     .188     .219 

.250 

.281 

.313 

.344 

1.50 

A 

.188 

.234     .281 

.328 

.375 

.422 

.469 

.516 

2.25 

i 

.250 

.313     .375 

.438 

.500 

.563, 

.625 

.688 

3.00 

iV        -313 

.391     .469     .547 

.625 

.703 

.781 

.859 

3.75 

f     i   .375 

.469 

.563     .656 

.750 

.844 

.938 

1.03 

4.50 

A        -438 

.547 

.656     .766 

.875 

.984 

1.09 

1.20 

5.25 

i     i   .500 

.625 

.750     .875 

1.00     1.13 

1.25 

1.38 

6.00 

TV       .563 

.703 

.844 

.984 

1.13     1.27 

1.41 

1.55 

6.75 

f     ;   .625 

.781 

.938   1.09 

1.25     1.41 

1.56 

1.72 

7.50 

-}-;,        .688 

.859 

1.03     1.20 

1.38     1.55 

1.72 

1.89 

8.25 

f        .750 

.938 

1.13     1.31 

1.50     1.69 

1.88 

2.06 

9.00 

it     '    -813 

1.02 

1.22 

1.42 

1.63     1.83 

2.03 

2.23 

9.75 

1         .875 

1.09 

1.31     1.53 

1.75 

1.97 

2.19 

2.41 

10.50 

f|        .938 

1.17 

1.41     1.64 

1.88 

2.11 

2.34 

2.58 

11.25 

1          1.00 

1.25 

1.50   jl.75 

2.00 

2.25 

2.50 

2.75 

12.00 

IrV      1-06 

1.33 

1.59   il.86 

2.13 

2.39 

2.66 

2.92 

12.75 

H 

1.13 

1.41 

1.69 

1.97 

2.25 

2.53 

2.81 

3.09 

13.50 

1.48 

1.78     2.08 

2.38     2.67 

2.97 

3.27 

14.25 

if      1JB5 

1.56 

1.88     2.19 

2.50 

2.81 

3.13 

3.44 

15.00 

I_PT     !  i  31 

1.64 

1.97     2.30 

2.63 

2.95 

3.28 

3.61 

15.75 

If       1.38 

1.72 

2.06 

2.41 

2.75 

3.09 

3.44 

3.78 

16.50 

IjV     !  !-44 

1.80 

2.16 

2.52 

2.88     3.23 

3.59 

3.95 

17.25 

1  1       1.50 

1.88 

2.25 

2.63 

3.00     3.38 

3.75 

4.13 

18.00 

IT? 

1.56 

1.95 

2.34 

2.73 

3.13 

3.52 

3.91 

4.30 

18.75 

If 

1.63 

2,03 

2.44 

2.84 

3.25 

3.66 

4.06 

4.47 

19.50 

144 

1.69 

2.11 

2.53     2.95     3.38     3.80 

4.22 

4.64 

20.25 

If 

1.75 

2.19    i  2.63     3.05     3.50 

3.94 

4.38 

4.81 

21.00 

lit 

1.81 

2.27 

2.72     3.17     3.63 

4.08 

4.53 

4.98 

21.75 

H 

1.88 

2.34 

2.81 

3.28 

3.75 

4.22 

4.69 

5.16 

22.50 

VH 

1.94 

2.42 

2.91 

3.39 

3.88 

4.36 

4.84 

5.33 

23.25 

2 

2.00 

2.50 

3.00 

3.50 

4.00 

4.50 

5.00 

5.50 

24.00 

i  , 

j 

tir 

AREAS  OP  PLAT  ROLLED  IRON. 

(CONTINUED.) 


Thickness 
in  Inches. 

8" 

SH" 

m» 

m» 

4" 

4V 

w 

4%" 

12" 

A 

.188 

.203 

.219 

.234 

.250 

.266 

.281 

.297 

.750 

.375 

.406 

.438 

.469 

.500 

.531 

.563 

.594 

1.50 

ft 

.563 

.609 

.656 

.703 

.750 

.797 

.844 

.891 

2.25 

.750 

.813 

.875 

.938 

1.00 

1.06 

1.13 

1.19 

3.00 

Jj 

.938 

1.02 

1.09 

1.17 

1.25 

1.33 

1.41 

1.48 

3.75 

3. 

1.13 

1.22 

1.31 

Ml 

1.50 

1.59 

1.69 

1.78 

4.50 

1 

1.31 

1.42 

1.53 

1.64 

1.75 

1.86 

1.97 

2.08 

5.25 

i 

1.50 

1.63 

1.75 

1.88 

2.00 

2.13. 

2.25 

2.38 

6.00 

_9^ 

1.69 

1.83 

1.97 

2.11 

2.25 

2.39 

2.53 

2.67 

6.75 

T 

1.88 

2.03 

2.19 

2.34, 

2.50 

2.66 

2.81 

2.97 

7.50 

ft 

2.06 

2.23 

2.41 

2.58 

2.75 

2.92 

3.09 

3.27 

8.25 

¥ 

2.25 

2.44 

2.63 

2.81 

3.00 

3.19 

3.38 

3.56 

9.00 

if 

2.44 

2.64 

2.84 

3.05 

3.25 

3.45 

3.66 

3.86 

9.75 

2.63 

2,84 

3.06 

3.28 

3.50 

3.72 

3.94 

4.16 

10.50 

A 

2.81 

3.05 

3.28 

3.52 

3.75 

8.98 

4.22 

4.45 

11.25 

• 

3.00 

3.25 

3.50 

3.75 

4.00 

4.25 

4.50 

4.75 

12.00 

i  y  ,y 

3.19 

3.45 

3.72 

3.98 

4.25 

4.52 

4.78 

5.05 

12.75 

i  i 

3.38 

3.66 

3.94 

4.22 

4.50 

4.78 

5.06 

5.34 

13.50 

4 

3.56 

3.86 

4.16 

4.45 

4.75 

5.05 

5.34 

5.64 

14.25 

u 

3.75 

4.06 

4.38 

4.69 

5.00 

5.31 

5.63 

5.94 

15.00 

IA 

3.94 

4.27 

4.59 

4.92 

5.25 

5.58 

5.91 

6.23 

15.75 

l1! 

4.13 

4.47 

4.81 

5.16 

5.50 

5.84 

6.19 

6.53 

16.50 

4.31 

4.67 

5.03 

5.39 

5.75 

6.11 

6.47 

6.83 

17.25 

if 

4.50 

4.88 

5.25 

5.63 

6.00 

6.38 

6.75 

7.13 

18.00 

l-9- 

4.69 

5.08 

5.47 

5.86 

6.25 

6.64 

7.03 

7.42 

18.75 

1.1 

4.88 

5.28 

5.69 

6.09 

6.50 

6.91 

7.31 

7.72 

19.50 

5.06 

5.48 

5.91 

6.33 

6.75 

7.17 

7.59 

8.02 

20.25 

i? 

5.25 

5.69 

6.13 

6.56 

7.00 

7.44 

7.88 

8.31 

21.00 

lit 

5.44 

5.89 

6.34 

6.80 

7.25 

7.70 

8.16 

8.61 

21.75 

11 

5.63 

6.09 

6.56 

7.03 

7.50 

7.97 

8.44 

8.91 

22.50 

1ft 

5.81. 

6.30 

6.78 

7.27 

7.75 

8.23 

8.72 

9.20 

23.25 

2 

6.00 

6.50 

7.00 

7.50 

8.00 

8.50 

9.00 

9.50 

24.00 

AREAS   OF  PLAT    ROLLED   IRON. 

(CONTINUED.) 


Thickness 
in  Inches. 

5" 

5*« 

5K» 

w 

6" 

w 

ey,» 

6^» 

12" 

.313 

.328 

.344 

.359 

.375 

.391 

.406 

.422 

.750 

1 

.625 

.656 

.688 

.719 

.750 

.781 

.813 

.844 

1.50 

.938 

.984 

1.03 

1.08 

1.13 

1.17 

1.22 

1.27 

2.25 

1 

1.25 

1.31 

1.38 

1.44 

1.50 

1.56 

1.63 

1.69 

3.00 

1.56 

1.64 

1.72 

1.80 

1.88 

1.95 

2.03 

2.11 

3.75 

I 

1.88 

1.97 

2.06 

2.16 

2.25 

2.34 

2.44 

2.53 

4.50 

A 

2.19 

2.30 

2.41 

2.52 

2.63 

£.73 

2.84 

2.95 

5.25 

2.50 

2.63 

2.75 

2.88 

3.00 

3.13 

3.25 

3.38 

6.00 

JL 

2.81 

2.95 

3.09 

3.23 

3.38 

3.52 

3.66 

3.80 

6.75 

1* 

3.13 

3.28 

3.44 

3.59 

3.75 

3.91 

4.06 

4.22 

7.50 

H 

3.44 

3.61 

3.78 

3.95 

4.13 

4.30 

4.47 

4.64 

8.25 

i 

3.75 

3.94 

4.13 

4.31 

4.50 

4.69 

4.88 

5.06 

9.00 

is 

4.06 

4.27 

4.47 

4.67 

4.88 

5.08 

5.28 

5.48 

9.75 

•' 

4.38 

4.59 

4.81 

5.03 

5.25 

5:47 

5.69 

5.91 

10.50 

1  5 

4.69 

49?, 

516 

5.39 

563 

586 

609 

6.33 

11.25 

1 

5.00 

5.25 

5.50 

5.75 

6.00 

6.25 

6.50 

6.75 

12.00 

IJL 

5.31 

5.58 

5.84 

6.11 

6.38 

6.64 

6.91 

7.17 

12.75 

lj 

5.63 

5.91 

6.19 

6.47 

6.75 

7.03 

7.31 

7.59 

13.50 

5.94 

6.23 

6.53 

6.83 

7.13 

7.42 

7.72 

8.02 

14.25 

H 

6.25 

6.58 

6.88 

7.19 

7.50 

,7.81 

8.13 

8.44 

15.00 

1?8 

6.56 

6.89 

7.22 

7.55 

7.88 

8.20 

8.53 

8.86 

15.75 

If 

6.88 

7.22 

7.56 

7.91 

8.25 

8.59 

8.94 

9.28 

16.50 

iA 

7.19 

7.55 

7.91 

8.27 

8.63 

8.98 

9.34 

9.70 

17.25 

H 

7.50 

7.88 

8.25 

8.63 

9.00 

9.38 

9.75 

10.13 

18.00 

1T9, 

7.81 

8.20 

8.59 

8.98 

9.38 

9.77 

10.16 

10.55 

18.75 

If 

8.13 

8.53 

8.94 

9.34 

9.75 

10.16 

10.56 

10.97 

19.50 

8.44 

8.86 

9.28 

9.70 

10.13 

10.55 

10.97 

11.39 

20.25 

If 

8.75 

9.19 

9.63 

10.00 

10.50 

10.94 

11.38 

11.81 

21.00 

l-U. 

9.06 

9.52 

9.97 

10.42 

10.88 

11.33 

11.78  ' 

12.23 

21.75 

if 

9.38 

9.84 

10.31 

10.78 

11.25 

11.72 

12.19 

12.66 

22.50 

9.69 

10.17 

10.68 

11.14 

11.63 

12.11 

12.59 

13.08 

23.25 

.& 

10.00 

10.50 

11.00 

11.50 

12.00 

12.50 

13.00 

13.59 

24.00 

r,     ..  , 

AREAS   OP  FLAT   ROLLED    IRON. 

(CONTINUED".) 


Thickness 
in  Inches. 

7// 

7>4'" 

1%" 

7&" 

8" 

aw 

8K" 

\*X" 

12" 

- 

A 

.438 

.453 

.469 

.484 

.500 

.516 

.531 

.547 

.750 

i 

.875 

.906 

.938 

.969 

1.00 

1.03 

1.06 

1.09 

1.50 

3 

1.31 

1.36 

1.41 

1.45 

1.50 

1.55 

1.59 

1.64 

2.25 

£ 

1.75 

1.81 

1.88 

1.94 

2.00 

2.06 

2.13 

2.19 

3.00 

A 

2.19 

2.27 

2.34 

2.42 

2.50 

2.58 

2.66 

2.73 

3.75 

I 

2.63 

2.72 

2.81 

2.91 

3.00 

3.09 

3.19 

3.28 

4.50 

TS 

3.06 

3.17 

3.28 

3.39 

3.50 

3.61 

3.72 

3.83 

5.25 

i 

3.50 

3.63 

3.75 

3.88 

4.00 

4.13 

4.25 

4.38 

6.00 

A 

3.94 

4.08 

4.22 

4.36 

4.50 

4.64 

4.78 

4.92 

6.75 

B 

8 

4.38 

4.53 

4.69 

4.84 

5.00 

5.16 

5.31 

5.47 

7.50 

« 

4.81 

4.98 

5.16 

5.33 

5.50 

5.67 

5.84 

6.02 

8.25 

3 

i 

5.25 

5.44 

5.63 

5.81 

6.00 

6.19 

6.38 

6.§6 

9.00 

H 

5.69 

5.89 

6.09 

6.30 

6.50 

6.70 

6.91 

7.11 

9.75 

6.13 

6.34 

6.56 

6.78 

7.00' 

7.22 

7.44 

7.66 

10.50 

16 

1  G 

6.56 

6.80 

7.03 

7.27 

7.50 

7.73 

7.97 

8.20 

11.25 

1 

7.00 

7.25 

7.50 

7.75 

8.00 

8.25 

8.50 

8.75 

12.00 

IrV 

7.44 

7.70 

7.97 

8.23 

8.50 

8.77 

9.03 

9.30 

12.75 

H 

7.88 

8.16 

8.44. 

8.72 

9.00 

9.28 

9.56 

9.84 

13.50 

IA 

8.31 

8.61. 

8.91 

9.20 

9.50 

9.80 

10.09 

10.39 

14.25 

11 

8.75. 

9.06 

9.38 

9.69 

10.00 

10.31 

10.63 

10.94 

15.00 

1& 

9.19 

9.52 

9.84 

10.17 

10.50 

10.83 

11.16 

11.48 

15.75 

U 

9.63 

9.97 

10.31 

10.66 

11.00 

11.34 

11.69 

12.03 

16.50 

i* 

10.06 

10.42 

10.78 

11.14 

11.50 

11.86 

12.22 

12.58 

17.25 

10.50 

10.88 

11.25 

11.63 

12.00 

12.38 

12.75 

13.13 

18.00 

iA 

10.94 

11.33 

11.72 

12.11 

12.50 

12.89 

13.28 

13.67 

18.75 

if 

11.38 

11.78 

12.19 

12.59 

13.00, 

13.41 

13.81 

14.22 

19.50 

IH 

11.81 

12.23 

12,66 

13.08 

13.50 

13.92 

14.34 

14.77 

20.25 

if 

12.25 

12.69 

13.13 

13.56 

14.00 

14.44 

14.88 

15.31 

21.00 

HI 

12.69 

13.14 

13.59 

14.05 

14.50 

14.95 

15.41 

15.86 

21.75 

u 

13.13 

13.59 

14.06 

14.53 

15.00 

15.47 

15.94 

16.41 

22.50 

1M 

13.56 

14.05 

14.53 

15.02 

15.50 

15.98 

16.47 

18.95 

23.25 

2 
i  

14.00 

14.50 

15.00 

15.50 

16.00 

16.50 

17.00 

17.50 

24.00 

AREAS   OP   FLAT   ROLLED    IRON. 

(CONTINUED.) 


Thickness 
in  Inches. 

9" 

w 

9K» 

9%" 

10" 

1CH" 

10i' 

'iOf 

: 

12" 

1 

1 

rV 

.563 

.578 

.594 

.609 

.625 

.641 

.651 

)'    .672 

75( 

i 

1.13 

1.16 

1.19 

1.22 

1.25 

1.28 

1.31 

1.34 

1.50 

j 

I  1.69 

1.73 

1.78 

1.83 

1.88 

1.92 

1.97 

2.02 

2.25 

i 

2.25 

2.31 

2.38 

2.44 

2.50 

2.56 

2.63 

2.69 

3.00 

A 

2.81 

2.89 

2.97 

3.05 

3.13 

3.20 

3.28 

3.36 

375 

3.38 

3.47 

3.56 

3.66 

3.75 

3.84 

3.94 

4.03 

4.50 

A- 

3.94 

4.05 

4.16 

4.27 

4.38 

4.48 

4.59 

4.70 

5.25 

4.50 

4.63 

4.75 

4.88 

5.00 

5.13 

5.25 

5.38 

6.00 

* 

5.06 

5.20 

5.34 

5.48 

5.63 

5.77 

5.91 

!  6.05 

675 

5.63 

5.78 

5.94 

6.09 

6.25 

6.41 

6.56 

'  6.72 

7.50 

A 

6.19 

6.36 

6.53 

6.70 

6.88 

7.05 

7.22 

7.39 

8.25 

i 

6??5 

6.94 

7.13 

7.31 

7.50 

7.69 

7.88 

1  8.06 

9.00 

it 

7.31 

7.52 

7.72 

7.92 

8.13 

8.33 

8.53 

!  8.73 

9.75 

¥ 

7.88 

8.09 

8.31 

8.53 

8.75 

8.97 

9.19 

:   9.41 

10.50 

M 

8.44 

8.67 

8.91 

9.14 

9.38 

9.61 

9.84 

10.08 

11.25 

i  " 

9.00 

9.25 

9.50 

9.75 

10.00 

10.25 

10.50 

10.75 

12.00 

H- 

9.56 

9.83 

10.09 

10.36 

10.63 

10.89 

11.16 

11.42 

12.75 

i1! 

10.13 

10.41 

10.69 

10.97 

11.25 

11.53 

11.81 

12.09 

13.50 

IA 

10.69  ! 

10.98 

11.28 

11.58 

11.88 

12.17 

12.47 

'12.77 

14.25 

11.25  ; 

11.56 

11.88 

12.19 

12.50 

12.81 

13.13 

,13.44 

15.00 

I  A 

11.81 

12.14 

12.47 

12.80 

13.13 

13.45 

13.78 

'14.11 

15.75 

if 

12.38 

12.72 

13.06 

13.41 

1375 

14.09 

14.44 

1478 

16.50 

12.94 

13.30 

13.66  : 

14.02 

14.38  ' 

14.73 

15.09 

15.45 

17.25 

H 

13.50  | 

13.88 

14.25  i 

14.63 

15.00 

j 

15.38 

15.75 

16.13 

18.00 

IA 

14.08 

14.45 

14.84  i 

15.23 

15.63  ! 

16.02 

16.41 

16.80 

18.75 

if 

14.63  ! 

15.03 

15.44 

15.84 

16.25  ! 

16.66 

17.06 

17.47 

19.50 

M* 

15.19 

15.61 

16.03 

16.45 

16.88 

17.30 

17.72 

18.14 

20.25 

it 

15.75 

16.19 

16.63  i 

17.06 

17.50 

17.94  . 

18.38 

18.81 

21.00 

HI 

16.31  i 

16.77 

17.22 

17.67 

18.13 

18.58 

19.03 

19.48 

2175 

1? 

16.88  i 

17.34  i 

17.81  ! 

18.28 

18.75  : 

19.22  ! 

19.69 

20.16 

22.50 

17.44  11 

t7.92  ! 

18.41 

1S.89 

19.38 

19.86  i 

20.34 

20.83 

23.25 

216 

13.00 

8.50 

19.00 

19.50 

20.00 

20.50 

21.00 

21.50 

24.00 

ft 

| 

i 

5  —                                                                                                        —  £ 
SQUARE  AND   ROUND   BARS. 

(CONTINUED.) 

Thickness 
or  Diameter 

in  Inches. 

2 

A 

:     Weight  of     ;     Weight  of 
[j  Bar            O  Bar 
:  One  Foot  long.  :  One  Foot  long. 

13.33         10.47 
14.18         11.14 
15.05         11.82 
15.95         12.53 

Area  of 
QBar 
in  sq.  inches. 

4.0000 
4.2539 
4.5156 
4.7852 

Area  of 
O  Bar 
in  sq.  inches. 

Circumference 
of  O  Bar 
in  inches. 

6.2832 
6.4795 
6.6759 
6,8722 

3.1416 
3.3410 
3.5466 
3.7583 

A 

,1 

16.88    1     13.25 
17.83         14.00 
18.80         14.77 
19.80    i     15.55 

5.0625 
5.3477 
5.6406 
5.9414 

3.9761 
4.2000 
4.4301 
4.6664 

7.0686 
7.2649 
7.4613 
7.6576 

l 

1 

11 

20.83         16.36 
21.89    !     17.19 
22.97    1     18.04 
24.08    !     18.91 

6.2500 
6.5664 
6.8906 

7.2227 

4.9087 
5.1572 
5.4119 
5.6727 

7.8540 
8.0503 
8.2467 
8.4430 

3 

1 

1  .! 

25.21         19.80 
26.37         20.71 
27.55    :     21.64 
28.76         22.59 

7.5625 
7.9102 
8.2656 
8.6289 

5.9396 
6.2126 
6.4918 
6.7771 

8.6394 
8.8357 
9.0321 
9.2284 

3 

A 

30.00        23.56 
31.26         24.55 
32.55         25.57 
33.87         26.60 

9.0000 
9.3789 
9.7656 
10.160 

7.0686 
7.3662 
7.6699 
7.9798 

9.4248 
9.6211 
9.8175 
10.014 

T 
"3 

35.21         27.65 
36.58         28.73 
37.97         29.82 
39.39    I     30.94 

10.563 
10.973 
11.391 
11.816 

8.2958 
8.6179 
8.9462 
9.2806 

10.210 
10.407 
10.603 
10.799 

1 
I 

I 

40.83    i     32.07 
42.30         33.23 
43.80         34.40 
45.33         35.60 

12.250 
12.691 
13.141 
13.598 

9.6211 
9.9678 
10.321 
10.680 

10.996 
11.192 
11.388 
11.585 

A 

w 

i  

46.88         36.82 
48.45         38.05 
50.05         39.31 
51.68         4O.59 

14.063 
14.535 
15.016 
15.504 

11.045 
11.416 
11.793 
12.177 

11.781 
11.977 
12.174 
12.370 

TV                                                                                                             fT 

SQUARE  AND   ROUND   BARS. 

(CONTINUED.) 

Thickness 
or  Diameter 
ill  Inches. 

Weight  of 
[jBar 
One  Foot  long. 

Weight  of 
O  Bar 

One  Foot  long. 

Area  of 
QBar 
in  sq.  inches. 

Area  of 
O  Bar 
in  sq.  inches. 

Circumference 
of  O  Bar 
in  inches. 

4 

i 

A 

53.33 
55.01 
56.72 
58.45 

41.89 
43.21 
44.55 
45.91 

16.000 
16.504 
17.016 
17.535 

12.566 
12.962 
13.364 
13.772 

12.566 
12.763 
12.959 
13.155 

! 

60.21 
61.99 
63.80 
65.64 

47.29 
48.69 
50.11 
51.55 

18.063 
18.598 
19.141 
19.691 

14.186 
14.607 
15.O33 
15.466 

13.352 
13.548 
13.744 
13.941 

f 

H 

67.50 
69.39 
71.30 
73.24 

53.01 
54.50 
56.00 
57.52 

20.250 
20.816 
21.391 
21.973 

15.904 
16.349 
16.800 
17.257 

14.137 
14.334 
14.530 
14.726 

I 

if 

75.21  •     59.07 
77.20       60.63 
79.22       62.22 
81.26       63.82 

22.563 
23.160 
23.766 
24.379 

17.721 
18.190 
18.665 
19.147 

14.923 
15.119 
15.315 
15.512 

! 

83.33 
85.43 
87.55 
89.70 

65.45 
67.10 
68.76 
70.45 

25.000 
25.629 
26.266 
26.910 

19.635 
20.129 
20.629 
21.135 

15.708 
15.904 
16.101 
16.297 

| 

91.88 
94.08 
96.30 
98.55 

72.16 
73.89 
75.64 
77.40 

27.563 
28.223 
28.891 
29.566 

21.648 
22.166 
22.691 
23.221 

16.493 
16.690 
16.886 
17.082 

| 

100.8 
103.1 
105.5 
107.8 

79.19 
81.00 
82.83 
84.69 

30.250 
30.941 
31.641 
32.348 

23.758 
24.301 
24.85O 
25.406 

17.279 
17.475 
17.671 
17.868 

1 

A 

110.2 
112.6 
115.1 
117.5 

86.56 
88.45 
90.36 
92.29 

33.063      25.967 
33.785      26.535 
34.516      27.109 
35.254      27.688 

18.064 
18.261 
18.457 
18.653 

106                          ^ 

*15  —                                                                                                        —  C 
SQUARE  AND   ROUND  BARS. 

(CONTINUED.) 

Thickness       Weight  of         Weight  of 

Area  of 

Area  of 

Circumference 

'    or  Diameter!      Q  Bar            Q  Bar 

[jBar 

O  Bar 

of  O  Bar 

in  Inches.  ;  One  Foot  long. 

One  Foot  long. 

in  sq.  inches. 

in  sq.  inches. 

in  inches. 

6 

120.0 

94.25 

36.000 

28.274 

18.850 

iV 

122.5 

96.22 

36.754 

28.866 

19.046 

Y          125.1 

98.22 

37.516 

29.465 

19.242 

•&         127.6 

100.2 

38.285 

30.069 

19.439 

i           130.2 

102.3 

39.063 

30.680 

19.635 

TV         132.8 

104.3 

39.848 

31.296 

19.831 

f          135.5        106.4 

40.641       31.919 

20.028 

7 
T¥ 

138.1 

108.5 

41.441 

32.548 

20.224 

1 

140.8 

110.6 

42.250      33.183 

20.420 

A         143.6 

112.7 

43.066       33.824 

20.617 

f 

146.3 

114.9 

43.891      34.472 

20.813 

li- 

149.1 

117.1 

44.723       35.125 

21.009 

f 

151.9 

119.3 

45.563      35.785 

21.206 

154.7 

121.5 

46.410 

36.450 

21.402 

? 

157.6 

123.7 

47.266 

37.122 

21.598 

§ 

160.4 

126.0 

48.129 

37.800 

21.795 

7 

163.3 

128.3 

49.000 

38.485 

21.991 

TV 

166.3 

130.6 

49.879 

39.175 

22.187 

i 

169.2 

132.9 

50.766 

39.871 

22.384 

A       172-2 

135.2 

51.660 

40.574 

22.58O 

T% 

175.2 
178.2 

137.6 
140.0 

52.563 
53.473 

41.282 
41.997 

22.777 
22.973 

3 

f 

181,3 

142.4 

54.391 

42.718 

23.169 

TV 

134.4 

144.8 

55.316 

43.445 

23.366 

187.5       147.3 

56.250 

44.179 

23.562 

190.6       149.7 

57.191 

44.918 

23.758 

| 

193.8 

152.2 

58.141 

45.664 

23.955 

11 

197.O 

154.7 

59.098 

46.415 

24.151 

i 

200.2 

157.2 

60.063 

47.173 

24.347 

It 

203.5 

159.8 

61.035 

47.937 

24.544 

} 

206.7 

162.4 

62.016 

48.707 

24.74O 

11         210.0 

T         i 

164.9 

63.004 

49.483 

24.936 

SQUARE  AND   ROUND   BARS. 

(CONTINUED.) 

Thickness 
or  Diameter 
in  Inches. 

Weight  of 
QBar 
One  Foot  long. 

Weight  of 
O  Bar 
One  Foot  long. 

Area  of              Area  of 
[J  Bar             O  Bar 
in  sq.  inches,     in  sq.  inches. 

Circumference 
of  O  Bar 

in  inches. 

8 

! 

213.3        167.6 
216.7         170.2 
220.1         172.8 
223.5         175.5 

64.000 
65.004 
66.016 
67.035 

50.265 
51.054 
51.849 
52.649 

25.133 
25.329 
25.525 
25.722 

i 

226.9 
230.3 
233.8 
237.3 

178.2 
180.9 
183.6 
186.4 

68.063 
69.098 
70.141 
71.191 

53.456 
54.269 
55.088 
55.914 

25.918 
26.114 
26.311 
26.507 

I 

240.8 
244.4 
248.0 
251.6 

189.2 
191.9 
194.8 
197.6 

72.250 
73.316 
74.391 
75.473 

56.745 
57.583 
58.426 
59.276 

26.704 
26.900 
27.096 
27.293 

it 
it 

255.2 
258.9 
262.6 
266.3 

200.4 
203.3 
206.2 
209.1 

76.563      60.132 
77.660      6O.994 
78.766      61.862 
79.879      62.737 

27.489 
27.685 
27.882 
28.078 

9 
t 

270.0 
273.8 
277.6 
281.4 

212.1 
215.0 
218.0 
221.0 

81.000      63.617 
82.129      64.504 
83.266      65.397 
84.410      66.296 

28.274 
28.471 
28.667 
28.863 

A 

285.2 
289.1 
293.0 
296.9 

224.0 
227.0 
230.1 
233.2 

85.563 
86.723 
87.891 
89.066 

67.201 
68.112 
69.029 
69.953 

29.060 
29.256 
29.452 
29.649 

I 

300.8 
304.8 
308.8 
312.8 

236.3 
239.4 
242.5 
245.7 

90.250 
91.441 
92.641 
93.848 

70.882 
71.818 
72.760 
73.708 

29.845 
30.041 
30.238 
30.434 

it 

,  * 

316.9 
321.0 
325.1 
329.2 

1 

248.9 
252.1 
255.3 
258.5 

95.063 
96.285 
97.516 
98.754 

74.662 
75.622 
76.589 
77.561 

30.631 
30.827 
31.023 
31.220 

SQTJAKE  AND  ROUN^&ff&ST 

(CONTTOTED.)      HUKIVBRS! 

Thickness 

Weight  of         Weight  of 

Area  of        ^^Dj 

m$$ 

or  Diameter 

[~]  Bar            O  Bar 

Q  Bar            O™^ 

•StEJac^ 

in  Inches. 

One  Foot  long,  i  One  Foot  long. 

in  sq.  inches.  \  in  sq.  inches. 

in  inches. 

10 

333.3 

261.8 

100.00 

78.540 

31.416 

TtT 

337.5 

265.1 

101.25 

79.525 

31.612 

341.7 

268.4 

102.52 

80.516 

31.809 

I 

346.0 

271.7 

103.79 

81.513 

32.005 

l 

350.2 

275.1 

105.06 

82.516 

32.201 

A 

354.5        278.4 

106.35 

83.525 

32.398 

358.8         281.8 

107.64 

84.541 

32.594 

rV 

363.1         285.2 

108.94 

85.562 

32.790 

} 

367.5 

288.6 

110.25       86.590 

32.987 

T9«T 

371.9    i     292.1 

111.57       87.624 

33.183 

I 

376.3 

295.5 

112.89       88.664 

33.379 

a 

380.7 

299.0 

114.22  |     89.710 

33.576 

|          385.2 

302.5 

115.56       90.763 

33.772 

if 

389.7 

306.1 

116.91 

91.821 

33.968 

i 

394.2 

309.6 

118.27 

92.886 

34.165 

ft         398.8 

313.2 

119.63 

93.956 

34.361 

11            403.3 

316.8 

121.00 

95.033 

34.558 

407.9 

320.4 

122.38       96.116 

34.754 

412.6 

324.0 

123.77       97.205 

34.95Q 

417.2 

327.7 

125.16       98.301 

35.147 

i 

~r 

421.9 

331.3 

126.56 

99.402 

35.343 

A 

426.6         335.0 

127.97 

100.51 

35.539 

1 

431.3        338.7 

129.39     101.62 

35.736 

TV 

436.1         342.5 

130.82 

102.74 

35.932 

440.8 

346.2 

132.25 

103.87 

36.128 

445.6 

350.0 

133.69 

105.00 

36.325 

f 

450.5 

353.8 

135.14 

106.14 

36.521 

tt 

455.3 

357.6 

136.60 

107.28 

36.717 

i 

I 

460.2 

361.4 

138.06 

108.43 

36.914 

if 

465.1         365.3 

139.54  |  109.59 

37.110 

1 

470.1         369.2 

141.02      110.75 

37.306 

it 

475.0        373.1 

142.50     111.92 

37.503 

WEIGHT   OF  SHEETS  OF  WROUGHT  IRON, 

STEEL,  COPPER  AND  BRASS.  (From  Haswell.) 

Weights  per  Square  Foot.    Thickness  by  Birmingham  Gauge. 

££        2SE         ^on.       |      Steel.          Copper. 

Brass. 

0000  i     .454 

18.22         18.46         20.57 

19.43 

000         .425 

17.05         17.28         19.25 

18.19 

00          .38 

15.25 

15.45         17.21         16.26 

0 

.34 

13.64 

13.82         15.40 

14.55 

1 

.3 

12.04 

12.20         13.59         12.84 

2 

.284 

11.40 

11.55         12.87         12.16 

3 

.259 

10.39 

10.53 

11.73         11.09 

4 

.238 

9.55 

9.68         10.78         10.19 

5 

.22 

8.83 

8.95           9.97 

9.42 

6 

.203 

8.15 

8.25           9.20 

8.69 

7 

.18 

7.22 

7.32           8.15 

7.70 

8 

.165 

6.62 

6.71 

7.47 

7.06 

9 

.148 

5.94 

6.02 

6.7O 

6.33 

10 

.134 

5.38 

5.45 

6.07 

5.74 

11 

.12 

4.82 

4.88 

5.44 

5.14 

12 

.109 

4.37 

4.43 

4.94 

4.67 

13 

.095 

3.81 

3.86 

4.30 

4.07 

14 

.083 

3.33 

3.37 

3.76 

3.55 

15 

.072 

2.89 

2.93 

3.26 

3.08 

16 

.065 

2.61 

2.64 

2.94           2.78 

17 

.058 

2.33 

2.36           2.63     i      2.48 

18 

.049 

1.97 

1.99 

2.22           2.10 

19 

.042 

1.69 

1.71 

1.90           1.80 

20 

.035 

1.40 

1.42 

1.59           1.50 

21 

.032 

1.28 

1.30           1.45           1.37 

22 

.028 

1.12           1.14           1.27           1.20 

23 

.025 

1.00           1.02           1.13           1.07 

24 

.022 

.883 

.895         1.00             .942 

25 

.02 

.803 

.813           .906           .856 

26 

.018 

.722 

.732           .815  1        .770 

27 

.016 

.642 

.651           .725           .685 

28 

.014 

.562 

.569 

.634           .599 

29 

.013 

.522 

.529           .589           .556 

30 

.012             .482 

.488           .544           .514 

31 

.01                .401 

.407           .453           .428 

32           .009             .361 

.366           .408           .385 

33           .008             .321           .325 

.362           .342 

34          .007             .281           .285 

.317           .300 

35           .005             .201           .203           .227           .214 

Specific  Gravity, 

7.704 

7.806 

8.698 

8.218 

Weight  Cubic  Foot, 

481.25 

487.75      543.6         513.6 

.       "         "    Inch, 

.2787         .2823         .3146!        .2972 

WEIGHT   OF 

SHEETS  OF  WROUGHT  IRON, 

STEEL,  COPPER  AND  BRASS.  (From  Haswell.) 

"Weights  per  Sq.  Foot. 

Thickness  by  American  (Browne  &  Sharpe's)  Gauge. 

No.  of           Thickness 
Gauge.          in  inches. 

Iron. 

Steel.           Copper. 

Brass. 

OOOO       .46 

18.46 

18.70 

20.84 

19.69 

000        .4096 

16.44 

16.66 

18.56 

17.53 

00         .3648 

14.64 

14.83 

16.53 

15.61 

0          .3249 

13.04 

13.21 

14.72 

13.90 

1          .2893 

11.61 

11.76 

13.11 

12.38 

2 

.2576 

10.34 

10.48 

11.67         11.03 

3 

.2294 

9.21 

9.33 

10.39 

9.82 

4          .2043 

8.20 

8.31            9.26 

8.74 

5          .1819 

7.30 

7.40           8.24           7.79 

6          .1620 

6.50 

6.59           7.34           6.93 

7          .1443 

5.79 

5.87           6.54           6.18 

8          .1285 

5.16 

5.22 

5.82            5.50 

9          .1144 

4.59 

4.65 

5.18           4.90 

10          .1019 

4.09 

4.14 

4.62            4.36 

11          .0907 

3.64 

3.69 

4.11 

3.88 

12          .0808 

3.24 

3.29 

3.66 

3.46 

13          .0720 

2.89 

2.93 

3.26 

3.08 

14          .0641 

2.57 

2.61 

2.90 

2.74 

15 

.0571 

2.29 

2.32 

2.59 

2.44 

16          .0508 

2.04 

2.07 

2.30 

2.18 

17          .0453 

1.82 

1.84 

2.05 

1.94 

18          .0403 

1.62 

1.64 

1.83 

1.73 

19 

.0359 

1.44 

1.46 

1.63 

1.54 

20 

.0320 

1.28 

1.30 

1.45 

1.37 

21 

.0285 

1.14 

1.16 

1.29 

1.22 

22 

.0253 

1.02 

1.03 

1.15            1.08 

23 

.0226 

.906 

.918 

1.02              .966 

24 

.0201 

.807 

.817 

.911            .860 

25 

.0179 

.718 

.728 

.811   i        .766 

26 

.0159 

.640 

.648 

.722 

.682 

27 

.0142 

.570 

.577 

.643 

.608 

28 

.0126 

.507 

.514 

.573 

.541 

29 

.0113 

.452 

.458 

.510 

.482 

30 

.0100 

.402 

.408 

.454 

.429 

31 

.0089 

.358 

.363 

.404 

.382 

32 

.0080 

.319 

.323 

.360 

.340 

33 

.0071 

.284 

.288 

.321 

.303 

34 

.O063 

.253 

.256 

.286 

.270 

35 

.0056 

.225 

.228 

.254 

.240 

As  there  sre  many  gauges  in  use  differing  from  each  other,  and  even  the  thicknesses  of  a 
certain  specified  gauge,  ss  the  Birmingham,  are  not  assumed  the  same  by  all  manufacturers, 
orders  for  sheets  ana  wire  should  always  state  the  weight  per  square  foot,  or  the  thickness 
^  in  thousandths  of  an  inch. 

AREAS  and  CIRCUMFERENCES  OF  CIRCLES. 

For  Diameters  from  -fe  to  100,  advancing  by  Tenths. 

Diam. 

Area. 

Circum. 

Diam. 

Area. 

Circum. 

0.0 

4.0 

12.5664 

12.5664 

.1 

.007854 

.31416 

.1 

13.2025 

12.8805 

.2 

.031416 

.62832 

.2 

13.8544 

13.1947 

.3 

.070686 

.94248 

.3 

14.5220 

13.5088 

.4 

.12566 

1.2566 

.4 

15.2053 

13.8230 

.5 

.19635 

1.5708 

.5 

15.9043 

14.1372 

.6 

.28274 

1.8850 

.6 

16.6190 

14.4513 

.7 

.38485 

2.1991 

.7 

17.3494 

147655 

.8 

.50266 

2.5133 

.8 

18.0956 

15.0796 

.9 

.63617 

2.8274 

.9 

18.8574 

15.3938 

1.0 

.7854 

3.1416 

5.0 

19.6350 

15.7080 

.1 

.9503 

3.4558 

.1 

20.4282 

16.0221 

.2 

1.1310 

3.7699 

.2 

21.2372 

16.3363 

.3 

1.3273 

4.0841 

.3 

22.0618 

16.6504 

j 

1.5394 

4.3982 

.4 

22.9022 

16.9646 

.5 

1.7671 

4.7124 

.5 

23.7583 

17.2788 

.6 

2.0106 

5.0265 

.6 

24.6301 

17.5929 

.7 

2.2698 

5.3407 

.7 

25.5176 

17.9071 

.8 

2.5447 

5.6549 

.8 

26.4208 

18.2212 

.9 

2.8353 

5.9690 

.9 

27.3397 

18.5354 

2.0 

3.1416 

6.2832 

6.0 

28.2743 

18.8496 

.1 

3.4636 

6.5973 

.1' 

29.2247 

19.1637 

.2 

3.8013 

6.9115 

.2 

30.1907 

19.4779 

.3 

4.1548 

7.2257 

.3 

31.1725 

19.7920 

.4 

4.5239 

7.5398 

.4 

32.1699 

i    20.1062 

.5 

4.9087 

7.8540 

.5 

33.1831 

20.4204 

.6 

5.3093     • 

8.1681 

.6 

34.2119 

20.7345 

.7 

5.7256 

8.4823 

.7 

35.2565 

21.0487. 

.8 

6.1575 

8.7965 

.8 

36.3168 

21.3628 

.9 

6.60521 

9.1106 

.9 

37.3928 

|    21.6770 

3.0 

7.0686 

9.4248 

7.0 

38.4845 

21.9911 

.1 

7.5477 

9.7389 

.1 

39.5919 

I    22.3053   . 

.2 

8.0425 

10.0531 

.2 

40.7150 

22.6195 

.3 

8.5530 

10.3673 

.3 

41.8539 

!     22.9336 

.4 

9.0792 

10.6814 

43.0084 

!    23.2478 

.5 

3.6211 

10.9956 

.5 

44.1786 

1    23.5619 

.6 

10.1788 

11.3097 

.6 

45.3646 

23.8761 

.7 

10.7521 

11.6239 

.7 

46.5663 

:    24.1903 

.8 

11.3411 

11.9381 

.8 

47.7836 

24.5044 

r         -9 

11.9459 

12.2522 

.9 

49.0167 

>     24.8186    . 

s 

1 

12 

JLJ  ""-                                                                                        a 

AKEAS  and  CIRCUMFERENCES  OF  CIRCLES. 

(CONTINUED.) 

Diam. 

Area. 

Circum. 

Diam. 

Area.           Circum. 

8.0           50.2655         25.1327 

12.0 

113.0973 

37.6991 

.1            51.5300         25.4469 

.1 

114.9901 

38.0133 

.2           52.8102         25.7611 

.2 

116.8987 

38.3274 

.3           54.1061         26.0752 

.3 

118.8229 

38.6416 

.4           55.4177        26.3894 

.4 

120.7628 

38.9557 

.5           56.7450 

26.7035 

.5 

122.7185 

39.2699 

.6 

58.0880 

27.0177 

.6 

124.6898 

39.5841 

.7 

59.4468 

27.3319 

.7 

126.6769 

39.8982 

.8 

60.8212 

27.6460 

.8 

128.6796 

40.2124 

.9 

62.2114 

27.9602 

.9 

130.6981 

40.5265 

9.0 

63.6173 

28.2743 

13.0 

132.7323 

40.8407 

.1 

65.0388 

28.5885 

.1 

134.7822 

41.1549 

.2 

66.4761 

28.9027 

.2 

136.8478 

41.4690 

.3 

67.9291 

29f2168 

.3 

138.9291 

41.7832 

.4 

69.3978 

29.5310 

.4 

141.0261 

42.0973 

.5 

70.8822 

29.8451 

.5 

143.1388 

42.4115 

.6 

72.3823 

30.1593 

.6 

145.2672 

42.7257 

.7 

73.8981 

30.4734 

.7 

147.4114 

43.0398 

.8 

75.4296 

30.7876 

.8 

149.5712 

43.3540 

•9, 

76.9769 

31.1018 

.9 

151.7468 

43.6681 

10.0 

78.5398 

31.4159 

14.0 

153.9380 

43.9823 

.1 

80.1185 

31.7301 

.1 

156.1450 

44.2965 

.2 

81.7128 

32.0442 

.2 

158.3677 

44.6106 

.3 

83.3229 

32.3584 

.3 

160.6061 

44.9248 

.4 

84.9487 

32.6726 

.4 

162.8602 

45.2389 

.5 

86.5901 

32.9867 

.5 

165.1300 

45.5531 

.6 

88.2473 

33.3009 

.6 

167.4155 

45.8673 

.7 

89.9202 

33.6150 

.7 

169.7167 

46.1814 

.8 

91.6088 

33.9292 

.8 

172.0336 

46.4956 

.9 

93.3132 

34.2434 

.9 

174.3662 

46.8097 

11.0 

95.0332 

34.5575 

15.0 

176.7146 

47.1239 

.1 

96.7689 

34.8717 

.1 

179.0786 

47.4380 

.2 

98.5203 

35.1858 

.2 

181.4584 

47.7522 

.3 

100.2875 

35.5000 

.3 

183.8539 

48.0664 

.4 

102.0703 

35.8142 

.4 

186.2650 

48.3805 

.5 

103.8689 

36.1283 

.5 

188.6919 

48.6947 

.6          105.6832 

36.4425 

.6 

191.1345 

49.0088 

.7         107.5132 

36.7566 

.7         193.5928 

49.3230 

.8          109.3588         37.0708 

.8         196.0668 

49.6372 

.9          111.2202     i    37.3850 

.9         198.5565         49.9513  c 

1 

3                                                  ^ 

8 

AREAS  and  CIRCUMFERENCES  OP  CIRCLES. 

(CONTINUED.) 

Diam.     Area. 

Circum. 

Diam. 

Area. 

Circum. 

16.0    201.0619 

50.2655 

20.0 

314.1593 

62.8319 

.1    203.5831 

50.5796 

.1 

317.3087 

63.1460 

.2    206.1199 

50.8938 

.2 

320.4739 

63.4602 

.3  ,  208.6724 

51.2080 

.3 

323.6547 

63.7743 

.4  !  211.2407 

51.5221 

.4 

326.8513 

64.0885 

.5    213.8246 

51.8363 

.5 

330'.0636 

64.4026 

.6    216.4243 

52.1504 

.6 

333.2916 

64.7168 

.7    219.0397 

52.4646 

.7 

336.5353 

65.0310 

.8    221.6708 

52.7788 

.8 

339.7947 

65.3451 

.9 

224.3176 

53.0929 

.9 

343.0698 

65.6593 

17.0    226.9801 

53.4071 

21.0 

346.3606 

65.9734 

.1   ;  229.6583 

53.7212 

.1 

349.6671 

66.2876 

.2    232.3522 

54.0354 

.2 

352.9894 

66.6018 

.3  i  235.0618 

54.3496 

.3 

356.3273 

66  9159 

.4  !  237.7871 

54.6637 

.4 

359.6809 

67.2301 

.5 

240.5282 

54.9779 

.5 

363.0503 

67.5442 

.6 

243.2849 

55.2920 

366.4354 

67.8584 

.7 

246.0574 

55.6062 

369.8361 

68.1726 

.8 

248.8456 

55.9203 

!s 

373.2526 

68.4867 

.9 

251.6494 

56.2345 

.9 

376.6848 

68.8009 

18.0 

254.4690 

56.5486 

22.0 

380.1327 

69.1150 

.1 

257.3043 

56.8628 

.1 

383.5963 

69.4292 

.2 

260.1553 

57.1770 

.2 

387.0756 

69.7434 

.3 

263.0220 

57.4911 

.3 

390.5707 

70.0575 

.4 

265.9044 

57.8053 

.4 

394.0814 

70.3717 

.5 

268.8025 

58.1195 

.5 

397.6078 

70.6858 

.6 

271.7164 

58.4836 

.6 

401.1500 

71.0000 

.7 

274.6459 

58.7478 

.7 

404.7078 

71.3142 

.8 

277.5911 

59.0619 

.8 

408.2814 

71.6283 

.9 

280.5521 

59.3761 

411.8707 

71.9425 

19.0 

283.5287 

59.6903 

23.0 

415.4756 

72.2566 

.1 

286.5211 

60.0044 

.1 

419.0963 

72.5708 

.2 

289.5292 

60.3186 

.2 

422.7327 

72.8849 

.3    292.5530 

60.6327 

.3 

426.3848 

73.1991 

.4    295.5925 

60.9469 

A 

430.0526 

73.5133 

.5 

298.6477 

61.2611 

.5 

433.7361 

73.8274 

.6    301.7186 

61.5752 

.6 

437.4354 

74.1416 

.7    304.8052 

61.8894 

.7 

441.1503 

74.4557 

.8  !  307.9075 

62.2035 

.8 

444.8809 

74.7699 

.9    311.0255 

62.5177 

.9 

448.6273 

75.0841  . 

11 

'>L 

?  —                                    —  " 

AREAS  and  CIRCUMFERENCES  OF  CIRCLES. 

(CONTINUED.) 

Diam. 

Area.     Circum. 

Diam. 

Area. 

Circum. 

24.0 

452.3893    75.3982 

28.0 

615.7522 

87.9646 

.1 

456.1671    75.7124 

.1 

620.1582 

88.2788 

.2 

459.9606    76.0265 

.2 

624.5800 

88.5929 

.3 

463.7698    76.3407 

.3 

629.0175 

88.9071 

.4 

467.5947    76.6549 

.4 

633.4707 

89.2212 

.5 

471.4352    76.9690 

.5 

637.9397 

89.5354 

.6 

475.2916    77.2832 

.6 

642.4243 

89.8495 

ry 

479.1636    77.5973 

.7 

646.9246 

90.1637 

is 

483.0513    77.9115 

.8 

651.4407 

90.4779 

.9 

486.9547    78.2257 

9 

655.9724 

90.7920 

25.0 

490.8739  '  78.5398 

29.0 

660.5199 

91.1062 

.1 

494.8087    78.8540 

.1 

665.0830 

91.4203 

a 

498.7592    79.1681 

.2 

669.6619 

91.7345 

Is 

502.7255    79.4823 

.3 

674.2565 

92.0487 

-  .4 

506.7075    79.7965 

.4 

678.8668 

92.3628 

.5 

510.7052    80.1106 

.5 

683.4928 

92.6770 

.6 

514.7185    80.4248 

.6 

688.1345 

92.9911 

.7 

518.7476    80.7389 

.7 

692.7919 

93.3053 

.8 

522.7924    81.0531 

.8 

697.4650 

93.6195 

.9 

526.8529    81.3672 

.9 

702.1538 

93.9336 

26.0 

530.9292    81.6814 

30.0 

706.8583 

94.2478 

.1 

535.0211    81.9956 

.1 

711.5786    94.5619 

.2 

539.1287    82.3097 

.2 

716.3145    94.8761 

.3 

543.2521    82.6239 

.3 

721.0662    95.1903 

.4 

547.3911    82.9380 

.4 

725.8336    95.5044 

.5 

551.5459    83.2522 

.5 

730.6167    95.8186 

.6 

555.7163    83.5664 

.6 

735.4154    96.1327 

.7 

559.9025    83.8805 

.7 

740.2299    96.4469 

.8 

564.1044    84.1947 

.8 

745.0601    96.7611 

.9 

568.3220    84.5088 

.9 

749.9060    97.0752 

27.0 

572.5553  !  84.8230 

31.0 

754.7676    97.3894 

.1 

576.8043    85.1372 

.1 

759.6450    97.7035 

.2 

581.0690    85.4513 

.2 

764.5380    98.0177 

.3 

585.3494    85.7655 

.3 

769.4467    98.3319 

.4 

589.6455  ;  86.0796 

.4 

774.3712    98.6460 

.5 

593.9574    86.3938 

.5 

779.3113    98.9602 

.6 

598.2849    86.7080 

.6 

784.2672    99.2743 

.7 

602.6282    87.0221 

.7 

789.2388    99.5885 

.8 

606.9871    87.3363 

.8 

794.2260    99.9026 

9   -9 

611.3618    87.6504 

.9 

799.2290   100.2168  , 

!  —                                           —  I 
AREAS  and  CIRCUMFERENCES  OF  CIRCLES. 

(CONTINUED.) 

Diam. 

Area. 

Oircum. 

Diam.    Area. 

Oircum. 

32.0    804.2477 

100.5310 

36.0   1017.8760  . 

113.0973 

.1 

809.2821 

100.8451 

.1 

1088.6887 

113.4115 

.2 

814.3322 

101.1593 

.2 

1029.2172 

113.7257 

.3 

819.3980 

101.4734 

.3 

1034.9113 

114.0398 

.4 

824.4796 

101.7876 

.4 

1040.6212 

114.3540 

.5 

829.5768 

102.1018 

.5 

1046.3467 

114.6681 

.6 

834.6898 

102.4159 

.6 

1052.0880 

114.9823 

.7 

839.8185 

102.7301 

.7 

1057.8449 

115.2965 

.8 

844.9628 

103.0442 

.8 

1063.6176 

115.6106 

.9 

850.1229 

103.3584 

.9 

1069.4060 

115.9248 

33.0 

855.2986 

103.6726 

37.0 

1075.2101 

116.2389 

.1 

860.4902 

103.9867 

.1 

1081.0299 

116.5531 

.2 

865.6973 

104.3009 

.2 

1086.8654 

116.8672 

.3 

870.9202 

104.6150 

.3 

1092.7166 

117.1814 

.4 

876.1588 

104.9292 

.4 

1098.5835 

117.4956 

.5 

881.4131 

105.2434 

£ 

1104.4662 

117.8097 

.6 

886.6831 

105.5575 

.6 

1110.3645 

118.1239 

.7 

891.9688 

105.8717 

.7 

1116.2786 

118.4380 

.8 

897.2703 

106.1858 

£ 

1122.2083 

118.7522 

.9 

902.5874 

106.5000 

.9 

1128.1538 

119.0664 

34.0 

907.9203 

106.8142 

38.0 

1134.1149 

119.3805 

.1 

913.2688 

107.1283 

.1 

1140.0918  '  119.6947 

.2 

918.6331 

107.4425 

.2 

1146.0844 

120.0088 

.3 

924.0131 

107.7566 

.3 

1152.0927 

120.3230 

.4 

929.4088 

108.0708 

.4 

1158.1167 

120.6372 

.5 

934.8202 

108.3849 

.5 

1164.1564 

120.9513 

.6 

940.2473 

108.6991 

.6 

1170.2118 

121.2655 

.7 

945.6901 

109.0133 

.7 

1176.2830 

121.5796 

.8 

951.1486 

109.3274 

.8 

1182.3698 

121.8938 

.9 

956.6228 

109.6416 

.9 

1188.4724 

122.2080 

35.0 

962.1128  - 

109.9557 

39.0 

1194.5906 

122.5221 

.1 

967.6184 

110.2699 

.1 

1200.7246 

122.8363 

.2 

973.1397 

110.5841 

.2 

1206.8742 

123.1504 

.3 

978.6768 

110.8982 

.3 

1213.0396 

123.4646 

.4 

984.2296 

111.2124 

.4 

1219.2207 

123.7788 

.5 

989.7980 

111.5265 

.5 

1225.4175 

124.0929 

.6 

995.3822 

111.8407 

.6 

1231.6300  '  124.4071 

.7 

1000.9821 

112.1549 

.7 

1237.8582   124.7212 

.8 

1006.5977 

112.4690 

.8 

1244.1021   125.0354 

.9 

1012.2290   112.7832 

.9    1250.3617  !  125.3495 

AREAS  and  CIRCUMFERENCES  OF  CIRCLES. 

i      (CONTINUED.) 

Diam. 

Area. 

Circum. 

Diam. 

Area. 

Circum. 

40.0 

1256.6371 

125.6637 

44.0   1520.5308 

138.2301 

.1 

1262.9281 

125.9779 

.1   1527.4502 

138.5442 

.2 

1269.2348 

126.2920 

.2   1534.3853 

138.8584 

.3  I  1275.5573 

126.6062 

.3 

1541.3360   139.1726 

.4   1281.8955 

126.9203 

.4 

1548.3025  ;  139.4867 

.5   1288.2493 

127.2345 

.5 

1555.2847   139.8009 

.6  1  1294.6189 

127.5487 

.6 

1562.2826   140.1153 

.7   1301.0042 

127.8628 

.7 

1569.2962   140.4292 

.8 

1307.4052 

128.1770 

.8 

1576.3255   140.7434 

.9 

1313.8219 

128.4911 

.9 

1583.3706   141.0575 

41.0 

1320.2543 

128.8053 

45.0 

1590.4313   141.3717 

.1 

1326.7024 

129.1195 

.1 

1597.5077  |  141.6858 

JB 

1333.1663 

129.4336 

.2 

1604.5999   142.0000 

.3 

1339.6458 

129.7478 

.3 

1611.7077   142.3142 

•4 

1346.1410 

130.0619 

.4 

1618.8313 

142.6283 

.5 

1352.6520 

130.3761 

.5 

1625.9705 

142.9425 

.6 

1359.1786 

130.6903 

.6 

1633.1255 

143.2566 

.7 

1365.7210 

131.0044 

.7 

1640.2962 

143.5708 

.8 

1372.2791 

131.3186 

.8 

1647.4826 

143.8849 

.9 

1378.8529 

131.6327 

.9 

1654.6847 

144.1991 

42.0 

1385.4424 

131.9469 

46.0 

1661.9025 

144.5133 

i 

1392.0476 

132.2611 

.1 

1669.1360 

144.8274 

J8 

1398.6685 

132.5752 

.2 

1676.3853 

145.1416 

.3 

1405.3051 

132.8894 

.3 

1683.6502 

145.4557 

.4   1411.9574  . 

133.2035 

.4 

1690.9308 

145.7699 

.5   1418.6254 

133.5177 

.5 

1698.2272 

146.0841 

.6 

1425.3092 

133.8318 

.6 

1705.5392 

146.3982 

.7 

1432.0086 

134.1460 

.7 

1712.8670 

146.7124 

.8 

1438.7838 

134.4602 

.8 

1720.2105   147.0265 

.9 

1445.4546 

134.7743 

.9 

1727.5697 

147.3407 

43.0 

1452.2012 

135.0885 

47.0 

1734.9445 

147.6550 

.1 

1458.9635 

135.4026 

.1 

1742.3351 

147.9690 

.2 

1465.7415 

135.7168 

.2 

1749.7414 

148.2832 

.3 

1472.5352 

136.0310 

.3 

1757.1635 

148.5973 

.4 

1479.3446 

136,3451 

.4 

1764.6012 

148.9115 

.5 

1486.1697 

136.6593 

.5 

1772.0546 

149.2257 

.6 

1493.0105 

136.9734 

.6   1779.5237   149.5398 

.7 

1499.8670 

137.2876 

.7 

1787.0086   149.8540 

.8   1506.7393 

137.6018 

.8 

1794.5091   150.1681 

.9  !  1513.6272 

137.9159 

.9    1802.0254   150.4823  . 

v  —                                    —  l, 

AREAS  and  CIRCUMFERENCES  OP  CIRCLES. 

(CONTINUED.) 

Diam. 

Area.     Circum. 

Diam. 

Area.     Circum. 

48.0 

1809.5574 

150.7964 

52.0 

2123.7166   163.3628 

.1 

1817.1050 

151.1106 

.1 

2131.8926  i  163.6770 

.2 

1824.6684 

151.4248 

.2 

2140.0843  :  163.9911 

.3 

1832.2475 

151.7389 

.3 

2148.2917   164.3053 

.4 

1839.8423 

152.0531 

.4 

2156.5149   164.6195 

.5 

1847.4528 

152.3672 

.5 

2164.7537   164.9336 

.6 

1855.0790 

152.6814 

.6 

2173.0082  i  165.2479 

.7 

1862.7210 

152.9956 

.7 

2181.2785  i  165.5619 

.8 

1870.3786 

153.3097 

.8 

2189.5644   165.8761 

.9 

1878.0519 

153.6239 

.9 

2197.8661   166.1903 

49.0 

1885.74C9 

163.9380 

53.0 

2206.1834  :  166.5044 

.1 

1893.4457 

154.2522 

.1 

2214.5165  :  166.8186 

.2 

1901.1662 

154.5664 

G) 

2222.8653  j  167.1327 

.3 

1908.9024 

154.8805 

]3 

2231.2298   167.4469 

.4 

1916.6543 

155.1947 

.4 

2239.6100   167.7610 

.5 

1924.4218 

155.5088 

.5 

2248.0059  i  168.0752 

.6 

1932.2051 

155.8230 

.6 

2256.4175   168.3894 

.7   1940.0042 

156.1372 

.7 

2264.8448   168.7035 

.8  !  1947.8189  1  156.4513 

.8 

2273.2879  :  169.0177 

.9 

1955.6493 

156.7655 

.9 

2281.7466   169.3318 

50.0 

1963.4954 

157.0796 

54.0 

2290.2210   169.6460 

.1 

1971.3572 

157.3938 

.1 

2298.7112   169.9602 

.2 

1979.2348   157.7080 

.2 

2307.2171   170.2743 

.3 

1987.1280   158.0221 

.3 

2315.7386   170.5885 

A 

1995.0370   158.3363 

.4 

2324.2759   170.9026 

.5 

2002.9617   158.6504 

.5 

2332.8289   171.2168 

.6   2010.9020   158.9646 

.6 

2341.3976   171.5310 

.7   2018.8581  !  159.2787 

.7 

2349.9820   171.8451 

.8   2026.8299   159.5929 

.8 

2358.5821   172.1593 

.9   2034.8174   159.9071 

.9 

2367.1979   172.4735 

51.0   2042.8206  i  160.2212 

55.0 

2375.8294  !  172.7876 

.1   2050.8395  \  160.5354 

.1 

2384.4767   173.1017 

.2   2058.8742   160.8495 

.2 

2393.1396   173.4159 

.3   2066.9245   161.1637 

.3 

2401.8183   173.7301 

.4   2074.9905   161.4779 

.4 

2410.5126  ,  174.0442 

£   2083.0723   161.7920 

.5 

2419.2227  !  174.3584 

.6  i  2091.1697   162.1062 

.6 

2427.9485   174.6726 

.7  I  2099.2829   162.4203 

.7 

2436.6899   174.9867 

.8  i  2107.4118   162.7345 

.8 

2445.4471  \  175.3009 

.9  !  2115.5563   163.0487     .9 

2454.2200  '  175.6150  , 

<  —                                    —  £ 

AREAS  and  CIRCUMFERENCES  OF  CIRCLES. 

(CONTINUED.) 

Diam. 

Area.     Circum. 

Diam.    Area.     Circum. 

56.0   2463.0086   175.9292 

60.0  ;  2827.4334   188.4956 

.1   2471.8130 

176.2433 

.1   2836.8660   188.8097 

.2   2480.6330 

176.5575 

.2   2846.3144   189.1239 

.3   2489.4687 

176.8717 

.3   2855.7784  ;  189.4380 

.4 

2498.3201 

177.1858 

.4 

2865.2582   189.7522 

.5 

2507.1873 

177.5000 

.5 

2874.7536  |  190.0664 

.6 

2516.0701 

177.8141 

.6 

2884.2648 

190.3805 

.7 

2524.9687 

178.1283 

.7 

2893.7917 

190.6947 

.8 

2533.8830 

178.4425 

.8 

2903.3343 

191.0088 

.9 

2542.8129 

178.7566 

.9 

2912.8926 

191.3230 

57.0 

2551.7586 

179.0708 

61.0 

2922.4686 

191.6372 

.1 

2560.7200 

179.3849 

.1 

2932.0563 

191.9513 

.2 

2569.6971 

179.6991 

.2 

2941.6617 

192.2655 

.3 

2578.6899 

180.0133 

.3 

2951.2828 

192.5796 

.4 

2587.6985 

180.3274 

.4 

2960.9197 

192.8938 

.5 

2596.7227 

180.6416 

.5 

2970.5722 

193.2079 

.6 

2605.7626 

180.9557 

.6 

2980.2405 

193.5221 

.7 

2614.8183 

181.2699 

.7 

2989.9244 

193.8363 

.8 

2623.8896 

181.5841 

.8 

2999.6241 

194.1504 

.9 

2632.9767 

181.8982 

.9 

3009.3395 

194.4646 

58.0 

2642.0794   182.2124 

62.0 

3019.0705 

194.7787 

.1 

2651.1979   182.5265 

.1 

3028.8173 

195.0929 

.2 

2660.3321   182.8407 

2 

3038.5798 

195.4071 

.3 

2669.4820  !  183.1549 

.3 

3048.3580 

195.7212 

.4 

2678.6476   183.4690 

.4    3058.1520 

196.0354 

.5 

2687.8289   183.7832 

.5   3087.9616 

196.3495 

.6 

2697.0259 

184.0973 

.6   3077.7869 

196.6637 

.7 

2708.2386 

184.4115 

.7   3087.6279 

196.9779 

.8 

2715.4670   184.7256 

.8   3097.4847 

197.2920 

.9   2724.7112   185.0398 

.9   3107.3571  i  197.6062 

59.0   2733.9710   185.3540 

63.0   3117.2453   197.9203 

.1   2743.2466   185.6681 

.1  :  3127.1492   198.2345 

.2   2752.5378  i  185.9823 

.2   3137.0688  I  198.5487 

.3   2761.8448   186.2964 

.3   3147.0040  !  198.8628 

.4   2771.1675   186.6106 

.4   3156.9550   199.1770 

.5   2780.5058   186.9248 

.5   3166.9217   199.4911 

.6   2789.8599  ,  187.2389 

.6   3176.9043  l,  199.8053 

.7  1  2799.2297  ,  187.5531 

.7   3186.9023 

200.1195 

.8   2808.6152  ;  187.8672 

.8   3196.9161 

200.4336 

.9   2818.0165   188.1814 

.9   3206.9456 

200.7478  , 

119                     «*- 

AREAS  and  CIRCUMFERENCES  OP  CIRCLES. 

(CONTINUED.) 

Diam. 

Area. 

Circum. 

Diam. 

Area.     Circum. 

64.0   3216.9909   201.0620 

68.0 

3631.6811  j  213.6283 

.1 

3227.0518   201.3761 

.1 

3642.3704  ,  213.9425 

.2 

3237.1285 

201.6902 

.2 

3653.0754   214.2566 

.3 

3247.2222 

202.0044 

.3 

3663.7960 

214.5708 

.4 

3257.3289 

202.3186 

.4 

3674.5324 

214.8849 

.5 

3267.4527 

202.6327 

.5 

3685.2845 

215.1991 

.6 

3277.5922 

202.9469 

.6 

3696.0523 

215.5133 

.7 

3287.7474 

203.2610 

.7 

3706.8359 

215.8274 

.8 

3297.9183 

203.5752 

.8 

3717.6351 

216.1416 

.9 

3308.1049 

203.8894 

.9 

3728.4500 

216.4556 

65.0 

3318.3072 

204.2035 

69.0 

3739.2807 

216.7699 

.1 

3328.5253 

204.5176 

.1 

3750.1270 

217.0841 

.2 

3338.7590 

204.8318 

.2 

3760.9891 

217.3982 

.3 

3349.0085 

205.1460 

.3 

3771.8668 

217.7124 

.4 

3359.2736 

205.4602 

.4 

3782.7603 

218.0265 

.5 

3369.5545 

205.7743 

.5 

3793.6695 

218.3407 

.6 

3379.8510 

206.0885 

.6 

3804.5944 

218.6548 

.7 

3390.1633 

206.4026 

.7 

3815.5350 

218.9690 

.8 

3400.4913 

206.7168 

.8 

3826.4913 

219.2832 

.9 

3410.8350 

207.0310 

.9 

3837.4633 

219.5973 

66.0 

3421.1944 

207.3451 

70.0 

3848.4510 

219.9115 

.1 

3431.5695 

207.6593 

.1 

3859.4544 

220.2256 

.2 

3441.9603 

207.9734 

.2 

3870.4736 

220.5398 

.3 

3452.3669 

208.2876 

.3 

3881.5084 

220.8540 

.4 

3462.7891 

208.6017 

.4 

3892.5590 

221.1681 

.5 

3473.2270 

208.9159 

.5 

3903.6252 

221.4823 

.6 

3483.6807 

209.2301 

.6 

3914.7072 

221.7964 

.7 

3494.1500 

209.5442 

.7 

3925.8049 

222.1106 

.8 

3504.6351 

209.8584 

.8 

3936.9182 

222.4248 

.9 

3515.1359 

210.1725 

.9 

3948.0473 

222.7389 

67,0 

3525.6524 

210.4867 

71.0 

3959.1921 

223.0531 

.1 

3536.1845 

210.8009 

.1 

3970.3526 

223.3672 

.2 

3546.7324 

211.1150 

.2 

3981.5289 

223.6814  t 

.3 

3557.2960 

211.4292 

.3 

3992.7208 

223.9956 

.4 

3567.8754 

211.7433 

.4 

4003.9284 

224.3097 

.5 

3578.4704 

212.0575 

.5 

4015.1518 

224.6239 

.6 

3589.0811 

•  212.3717 

.6 

4026.3908 

224.9380 

.7 

3599.7075 

212.6858 

.7 

4037.6456 

225.2522 

.8 

3610.3497 

213.0000 

.8 

4048.9160 

225.5664 

.   .9 

3621.0075 

21&3141 

.9 

4060.2022 

225.8805  , 

AREAS  and  CIRCUMFERENCES  OP  CIRCLES. 

(CONTINUED.) 

Diam. 

Area. 

Circum. 

Diam. 

Area. 

Circum. 

72.0 

4071.5041 

226.1947 

76.0 

4536.4598 

238.7610 

.1 

4082.8217 

226.5088 

.1 

4548.4057   239.0752 

.2 

4094.1550 

226.8230 

.2 

4560.3673 

239.3894 

4105.5040 

227.1371 

.3 

4572.3446 

239.7035 

'.4 

4116.8687 

227.4513 

.4 

4584.3377 

240.0177 

.5 

4128.2491 

227.7655 

.5 

4596.3464 

240.3318 

.6 

4139.6452 

228.0796 

.6 

4608.3708 

240.6460 

.7 

4151.0571 

228.3938 

.7 

4620.4110 

240.9602 

.8 

4162.4846 

228.7079 

.8 

4632.4669 

241.2743 

.9 

4173.9279 

.  229.0221 

.9 

4644.5384 

241.5885 

73.0 

4185.3868 

229.3363 

77.0 

4656.6257 

241.9026 

.1 

4196.8615 

229.6504 

.1 

4668.7287 

242.2168 

.2 

4208.3519 

229.9646 

.2 

4680.8474 

242.5310 

.3 

4219.8579 

230.2787 

.3 

4692.9818 

242.8451 

.4 

4231.3797 

230.5929 

.4 

4705.1319 

243.1592 

.5 

4242.9172 

230.9071 

.5 

4717.2977 

243.4734 

.6 

4254.4704 

231.2212 

.6 

4729.4792 

243.7876 

.7 

4266.0394 

231.5354 

"7 

4741.6765 

244.1017 

.8 

4277.6240 

231.8495- 

£ 

4753.8894 

244.4159 

.9 

4289.2243 

232.1637 

.9 

4766.1181 

244.7301 

74.0 

4300.8403 

232.4779 

78.0 

4778.3624 

245.0442 

A 

4312.4721 

232.7920 

.1 

4790.6225 

245.3584 

9 

•& 

4324.1195 

233.1062 

.2 

4802.8983 

245.6725 

.3 

4335.7827 

233.4203 

.3 

4815.1897 

245.9867 

.4 

.4347.4616 

233.7345 

.4 

4827.4969 

246.3009 

.5 

4359.1562 

234.0487 

.5 

4839.8198 

246.6150 

.6 

4370.8664 

234.3628 

.6 

4852.1584 

246.9292 

.7 

4382.5924 

234.6770 

.7 

4864.5128   247.2433 

.8 

4394.3341 

234.9911 

.8 

4876.8828   247.5575 

.9 

4406.0916 

235.3053 

.9 

4889.2685  1  247.8717 

75.0 

4417.8647 

235.6194 

79.0   4901.6699   248.1858 

.1 

'  4429.6535 

235.9336 

.1  i  4914.0871  !  248.5000 

.2 

4441.4580 

236.2478 

.2  !  4926.5199   248.8141 

.3 

4453.2783 

.  236.5619 

.3   4938.9685   249.1283 

.4 

4465.1142 

236.8761 

.4  i  4951.4328   249.4425 

.5 

4476.9659 

237.1902 

.5   4963.9127   249.7566 

.6 

4488.8332 

237.5044 

.6   4976.4084  ,  250.0708 

.7 

4500.7163 

237.8186 

.7   4988.9198   250.3850 

.8 

4512.6151 

238.1327 

.8   5001.4469   250.6991 

.9 

4524.5296 

238.4469 

.9   5013.9897   251.0133 

J  —                                    —  E 

AREAS  and  CIRCUMFERENCES  OF  CIRCLES. 

(CONTINUED.) 

Diam. 

Area. 

Circum. 

Diam.    Area. 

Circum. 

80.0   5026.5482 

251.3274 

84.0   5541.7694 

263.8938 

.1    5039.1225 

251.6416 

.1   5554.9720 

264.2079 

.2   5051.7124 

251.9557 

.2   5568.1902 

264.5221 

.3   5064.3180 

252.2699 

.3   5581.4242 

264.8363 

.4   5076.9394 

252.5840 

.4 

5594.6739   285.1514 

.5   5089.5764 

252.8982 

.5 

5607.9392   265.4646 

.6   5102.2292 

253.2124 

.6 

5821.2203 

265.7787 

.7   5114.8977 

253.5265 

.7 

5634.5171 

266.0929 

.8   5127.5819 

.253.8407 

.8 

5647.8296 

266.4071 

.9   5140.2818 

254.1548 

.9 

5661.1578 

266.7212 

81.0   5152.9973 

254.4690 

85.0 

5874.5017 

267.0354 

.1   5165.7287 

254.7832 

.1 

5687.8614 

267.3495 

.2   5178.4757 

255.0973 

.2 

5701.2367 

267.6637 

.3  |  5191.2384 

255.4115 

.3 

5714.6277 

267.9779 

.4   5204.0168 

255.7256 

.4 

5728.0345 

268.2920 

.5  !  5216.8110 

256.0398 

.5 

5741.4569 

268.6062 

.6   5229.6208 

256.3540 

.6 

5754.8951 

268.9203 

.7   5242.4463 

256.6681 

.7 

5768.3490 

269.2345 

.8   5255.2876 

256.9823 

.8 

5781.8185 

269.5486 

.9   5268.1446 

257.2966 

.9 

5795.3038   269.8628 

82.0 

5281.0173 

257.6106 

86.0 

5808.8048   270.1770 

.1 

5293.9056 

257.9247 

.1 

5822.3215   270.4911 

.2 

5308.8097 

258.2389 

.2 

5835.8539   270.8053 

.3 

5319.7295 

258.5531 

.3 

5849.4020  j  271.1194 

.4 

5332.6650 

258.8672 

.4 

5862.9659  :  271.4336 

.5 

5345.6162 

259.1814 

.5 

5876.5454  !  271.7478 

.6 

5358.5832 

259.4956 

.6 

5890.1407  :  272.0619 

.7 

5371.5658 

259.8097 

.7 

5903.7516  1  272.3761 

.8 

5384.5641 

280.1239 

.8   5917.3783  1  272.6902 

.9 

5397.5782 

260.4380 

.9   5931.0208  i  273.0044 

83.0 

5410.6079 

260.7522 

87.0  i  5944.6787  '  273.3186 

.1 

5423.6534 

261.0663 

.1  '  5958.3525  i  273.6327 

.2 

5436.7146 

261.3805 

.2   5972.0420  !  273.9469 

.3 

5449.7915 

261.6947 

.3   5985.7472  ;  274.2610 

.4 

5462.8840 

262.0088 

.4   5999.4681   274.5752 

.5 

5475.9923 

262.3230 

.5   6013.2047   274.8894 

.6   5489.1163 

262.6371 

.6   6026.9570   275.2035 

.7   5502.2561 

262.9513 

.7  i  6040.7250  !  275.5177 

.8   5515.4115 

263.2655 

.8  i  6054.5088  !  275.8318 

.9   5528.5826 

263.5796 

.9   6088.3082  :  276.1460  . 

AREAS  and  CIRCUMFERENCES  OF  CIRCLES, 

(CONTINUED.) 

Diam. 

Area. 

Circum. 

Diam. 

Area. 

Circum. 

88.0   6082.1234 

276.4602 

92.0 

6647.6101 

289.0265 

.1 

6095.9542 

276.7743 

.1 

6662.0692 

289.3407 

.2 

6109.8008 

277.0885 

.2 

6676.5441 

289.6548 

.3 

6123.6631 

277.4026 

.3 

6691.0347 

289.9690 

.4 

6137.5411 

277.7168 

.4 

6705.5410 

290.2832 

.5 

6151.4348 

278.0309 

.5 

6720.0630   290.5973 

.6 

6165.3442 

278.3451 

.6 

6734.6008 

290.9115 

.7 

6179.2693 

278.6593 

.7 

6749.1542 

291.2256 

.8 

6193.2101 

278.9740 

.8 

6763.7233   291.5398 

.9 

6207.1666 

279.2876 

.9 

6778.3082  !  291.8540 

89.0 

6221.1389 

279.6017 

93.0 

6792.9087  I  292.1681 

.1 

6235.1268 

279.9159 

.1 

6807.5250   292.4823 

.2 

6249.1304 

280.2301 

.2 

6822.1569   292.7964 

.3 

6263.1498 

280.5442 

.3 

6836.8046   293.1106 

.4 

6277.1849 

280.8584 

.4 

6851.4680   293.4248 

.5 

6291.2356 

281.1725 

.5 

6866.1471   293.7389 

.6 

6305.3021 

281.4867 

.6 

6880.8419   294.0531 

.7 

6319.3843 

281.8009 

.7 

6895.5524 

294.3672 

.8 

6333.4822 

282.1150 

.8 

6910.2786 

294.6814 

.9 

6347.5958 

282.4292 

.9 

6925.0205   294.9956 

90.0 

6361.7251 

282.7433 

94.0 

6939.7782 

295.3097 

.1 

6375.8701 

283.0575 

.1 

6954.5515 

295.6239 

.2 

6390.0309 

283.3717 

.2 

6969.3106   295.9380 

.3 

6404.2073 

283.6858 

.3 

6984.1453  i  296.2522 

.4 

6418.3995 

284.0000 

.4 

6998.9658 

296.5663 

.5 

6432.6073 

284.3141 

.5 

7013.8019 

296.8805 

.6 

6446.8309 

284.6283 

.6 

7028.6538 

297.1947 

.7 

6461.0701   284.9425 

.7 

7043.5214 

297.5088 

.8 

6475.3251   285.2566 

.8 

7058.4047 

297.8230 

.9 

6489.5958 

285.5708 

.9 

7073.3033  • 

298.1371 

91.0 

6503.8822 

285.8849 

95.0 

7088.2184 

298.4513 

.1 

6518.1843  ' 

286.1991 

.1 

7103.1488 

298.7655 

.2 

6532.5021 

286.5183 

.2 

7118.1950 

299.0796 

.3 

6546.8356 

286.8274 

.3 

7133.0568 

299.3938 

.4 

6561.1848 

287.1416 

.4 

7148.0343 

299.7079 

.5 

6575.5498 

287.4557 

.5 

7163.0276 

300.0221 

.6 

6589.9304 

287.7699 

.6 

.7178.0366 

300.3363 

.7 

6604.3268 

288.0840 

.7 

7193.0612 

300.6504 

.8 

6618.7388 

288.3982 

.8 

7208.1016 

300.9646 

n  -  '9 

6633.1666 

288.7124 

.9 

7223.1577 

301.2787  . 

AREAS  and  CIRCUMFERENCES  OF  CIRCLES. 

(CONTINUED.) 


Diam. 

Area. 

Circum. 

Diam. 

Area. 

Circum. 

96.0 

7238.2295 

301.5929 

98.0 

7542.9640 

1  307.8761 

.1 

7253.3170 

301.9071 

.1 

7558.3656 

,  308.1902 

.2 

7268.4202 

302.2212 

.2 

7573.7830 

!  308.5044 

.3 

7283.5391  - 

302.5354 

.3 

7589.2161 

308.8186 

.4 

7298.6737 

302.8405 

.4 

7604.6648 

309.1327 

.5 

7313.8240 

303.1637 

.5 

7620.1293 

309.4469 

.6 

7328.9901 

303.4779 

.6 

7635.6095 

309.7610 

.7 

7344.1718 

303.7920 

.7 

7651.1054 

310.0752 

.8 

7369.3693 

304.1062 

.8 

7666.6170 

310.3894 

.9 

7374.5824 

304.4203 

.9 

7682.1444 

i  310.7035 

97.0 

7389.8113 

304.7345 

99.0 

7697.6893 

311.0177 

.1 

7405.0559 

305.0486 

.1 

7713.2461 

1  311.3318 

.2 

7420.3162 

305.3628 

.2 

7728.8206 

311.6460 

.3 

7435.5922 

305.6770 

.3 

7744.4107 

311.9602 

.4 

7450.8839 

305.9911 

.4 

7760.0166 

312.2743 

.5 

7466.1913 

306.3053 

.5 

7775.6382 

312.5885 

.6 

7481.5144 

306.6194 

.6 

7791.2754 

312.9026 

ty 

7496.8532 

306.9336 

.7 

7806.9284 

313.2168 

.'s 

7512.2078 

307.2478 

.8 

7822.5971 

313.5309 

.9 

7527.5780 

307.5619 

.9 

7838.2815 

313.8451 

100.0 

7853.9816 

314.1593 

To  compute  the  area  or  circumference  of  a  diameter  greater 
than  100  and  less  than  1001 : 

^Takeout  the  area  or  circumference  from  table  as  though  the 
m^H&erliacl  one  decimal,  and  move  the  decimal  point  two  places 
to  the  right  for  the  area,  and  one  place  for  the  circumference. 

EXAMPLE— Wanted  the  area  and  circumference  of  567.  The  tabular  area  for  56.7 
is  2524.9687;  and  circumference  178.1283.  Therefore  area  of  567  =  252496.87  and 
circumference  =  1781.283. 

To  compute  the  area  or  circumference  of  a  diameter  greater 
than  1000: 

Divide  by  a  factor,  as  2,  3,  4,  5,  etc.,  if  practicable,  that  will 
leave  a  quotient  to  be  found  in  table,  then  multiply  the  tabular 
area  of  the  quotient  by  the  sqtiare  of  the  factor,  or  the  tabular 
circumference  by  the  factor. 

EXAMPLE— Wanted  the  area  and  circumferenee  of  2109.  Dividing  by  3,  the  quotient 
is  703,  for  which  the  area  is  388150.84  and  the  circumference  2208.54.  Therefore  area 
of  2109  =  388150.84  X  9  =  3493357.56  and  circumference  =  2208.54  X  3  =  6625.62. 

124 


WEIGHT  OF  RIVETS,  and  ROUND  HEADED 

BOLTS  WITHOUT  NUTS,  PER  100. 

Length  from  under  head.            One  cubic  foot  weighing  480  Ibs. 

Length. 

yi, 

1A"     V      %"      W  ''•    1"      l}«"  •  1^" 

Inches. 

Dia. 

Dia.       Dia.       Dia. 

Dia. 

Dia.       Dia.       Dia. 

Ijf 

5.4 

12.6       21.5 

28.7 

43.1 

65.3       91.5      123. 

1/12    ; 

6.2 

13.9       23.7 

31.8 

47.3 

70.7       98.4 

133. 

IX 

6.9 

15.3 

25.8 

34.9 

51.4 

76.2     105. 

142. 

2 

7.7 

16.6 

27.9 

37.9 

55.6 

81.6     112. 

150. 

2^  ^ 

8.5 

18.0 

30.0 

41.0 

59.8 

87.1 

119. 

159. 

2^1 

9.2 

19.4 

32.2       44.1 

63.0 

92.5 

126. 

167. 

10.0     20.7 

34.3       47.1 

68.1' 

98.0 

133. 

176. 

34 

10.8  i  22.1 

36.4  j    50.2 

72.3 

103. 

140. 

.184. 

3J4 

11.5      23.5 

38.6       53.3 

76.5 

109. 

147.       193. 

3X 

12.3     24.8       40.7       56.4       80.7     114. 

154.    I  201. 

3% 

13.1  i  26.2       42.8       59.4       84.8     120. 

161.     i  210. 

4 

13.8     27.5  ;    45.0       62.5  \    89.0  ,  125. 

167.    !  218. 

4^ 

14.6  i  28.9  '    47.1 

65.6  !    93.2     131. 

174.       227. 

41^ 

15.4      30.3  i    49.2 

68.6  !    97.4     136. 

181.    ;  236. 

4% 

16.2      31.6       51.4 

71.7 

102. 

142. 

188.       244. 

5 

16.9      33.0      53.5 

74.8 

106. 

147. 

195. 

253. 

5M 

17.7 

34.4 

55.6 

77.8 

110. 

153. 

202. 

261. 

5)-^ 

18.4 

35.7 

57.7 

80.9 

114. 

158.    !  209. 

270. 

5% 

19.2 

37.1 

59.9 

84.0 

118. 

163. 

216. 

278. 

6 

20.0 

38.5 

62.0      87.0 

122. 

169. 

223. 

287. 

6j£ 

21.5     41.2 

66.3 

93.2 

131. 

180. 

236. 

304. 

7  " 

23.0     43.9 

70.5 

99.3 

139. 

191. 

250. 

321. 

7/12 

24.6 

46.6 

74.8 

106. 

147. 

202. 

264. 

338. 

8 

26.1      49.4 

79.0 

112. 

156. 

213. 

278. 

355. 

S1^ 

27.6 

52.1 

83.3 

118. 

164. 

223. 

292. 

372. 

9" 

29.2 

54.8 

87.6 

124. 

173. 

234. 

306. 

389. 

9}<2 

30.7 

57.6 

91.8 

130. 

181. 

245. 

319. 

406. 

10 

32.2 

60.3 

96.1 

136. 

189. 

256. 

333. 

423. 

1()1£ 

33.8 

63.0 

101. 

142. 

198. 

267. 

347. 

440. 

11 

35.3 

65.7 

105. 

148. 

206. 

278. 

361. 

457. 

ll/^ 

36.8 

68.5 

109. 

155. 

214. 

289. 

375. 

474. 

12 

38.4 

71.2 

113. 

161. 

223. 

300. 

388. 

491. 

Heads. 

1.8 

5.7 

10.9 

13.4' 

22.2 

38.0 

57.0 

82.0 

v 

I 

"Yj 

UPSET    SCREW    ENDS    FOR 

ROUND    AND 

SQUARE   BARS. 

Standard  Proportions  of  the  Keystone  Bridge  Company. 

Dia.  of 
Round  or 
Side  of 
Square 
Bar. 
Inches. 

ROUND    BARS. 

SQUARE    BARS. 

Dia.  of 

Upset 
Screw 
End. 
Inches. 

Dia.  of 

Screw  at 
Root  of 
Thread. 
Inches. 

Threads 
per  Inch. 
No. 

Excess  of 
Effective 
Area  of 
Screw  End 
over  Bar. 
Per  Cent. 

Dia.  of 
Upset 
Screw 
End. 
Inches. 

Dia.  of 

Screw  at 
Root  of 
Thread. 
Inches. 

Excess  of 
Threads  i  ^J™ 

0<      t  over  Bar. 
j  Per  Cent. 

A 

X  •    .620  i   10 
X       -620      10 

54 
21 

I 

.620 
.731 

10           21 
9           33 

If 

%       .731       9           37 
1           .837       8           48 

i 
i 

.837       8           41 
.837       8           17 

it 

1          .837       8 
1M       .940  i     7 

25 
34 

W 

.940       7 
1.065       7 

23 
35 

i! 

IK  !  1.065       7 
W  !  1.065       7 

48 
29 

1 

1.160       6 
1.160-      6 

38 
20 

i 
IA 

IK     1-160       6 
1%     1-160       6 

35 
19 

!» 

1.284       6 
1.389       5^ 

29 
34 

j¥ 

1)1 

1.284 
1.284 

6 
6 

30 
17 

IS 

1.389       5^ 
1.490       5 

20 

24 

IA 

}| 

1.389 
1.490 

5  2 

23 
29 

11 

1.615 
1.615 

5 
5 

31 
19 

}g 

i 

1.490 
1.615 

5 
5 

18 
26 

2 

1.712 
1.837 

*& 

22 
28 

IA 

2 
2 

1.712 
1.712 

$ 

36 
20 

1! 

1.837 
1.962 

•*& 

18 
24 

iff 

% 

1.837 
1.837 

$ 

28 
18 

If 

2.087 
2.087 

4K 

80 
20 

Iff. 

3$ 

1.962 
1.962 

*% 

26 
17 

9  1/ 

673 

2.175 
2.300 

4 

4 

21 
26 

i 

S* 

2,087 

2.175 

4  2 

24 
26 

i 

2.300 
2.425 

4 
4 

18 
23 

2 

If 

2.175  i     4 
2.300       4 

18 
24 

2% 

2.550 
2.550 

4 
4 

28 
20 

1 

2.300 
2.425 

j 

4 

17 
23 

fc. 

2.629 
2.754 

1 

20 
24 

^TJ 

UPSET    SCREW   ENDS. 

(CONTINUED.) 

Dia.  of 

ROUND    BARS. 

SQUARE    BARS. 

Round  or 
Side  of 
Square 
Bar. 
Inches. 

Dia.  of      Dia.  of 
Upset     Screw  at 
Screw      Root  of 
End.   ;   Thread. 
Inches.     Inches. 

Threads 
per  Inch. 
No. 

Excess  of 
Effective 
Area  of 
Screw  End 
over  Bar. 
Per  Cent. 

Dia.  of 
Upset 
Screw 
End. 
Inches. 

Dia.  of 
Screw  at 
Root  of 
Thread. 
Inches. 

Threads 
per  Inch. 

No. 

Excess  of 
Effective 
Area  of 
Screw  End 
over  Bar. 
Per  Cent. 

~2K~ 

27« 

2.550 

4 

28 

m 

2.754 

3K 

18 

2fV 

2% 

2.550 

4 

22 

3% 

2.879 

3/1 

22 

gS/ 

3 

2.629 

3^ 

23 

3% 

3.004 

3K 

26 

gJL 

3)8 

2.754 

3>2 

28 

3.004 

3jl> 

19 

l% 

3^5 

2.754 

21 

3M 

3.100 

3^  I     21 

3}^     2.879 

3J£ 

26 

3^ 

3.225 

3K       24 

2% 

3i/ 

2.879 

3>£ 

20 

3% 

3.225 

314        19 

3K 

3.004 

3K 

25 

8g 

3.317 

3 

20 

2% 

3/8 

3.004 

3/£ 

19 

3K 

3.442 

3    , 

23 

3>£ 

3.100 

3^ 

22 

% 

3.442 

3 

18 

2% 

3% 

3.225 

3^f 

26 

4 

3.567 

3 

21 

3.225 

3K 

21 

413 

3.692 

3 

24 

3 

32/ 

3.317 

3 

22 

438' 

3.692 

3 

19 

3% 

3.442 

3 

21 

3.923 

2% 

24 

3L/    ! 

4 

3.567 

3 

20 

4% 

4.028 

2% 

21 

3M 

4>8 

3.692 

3- 

20 

4%$ 

4.153 

19 

3^ 

414 

'3.798 

2% 

18 

3% 

4/i> 

4.028 

23 

3K 

w 

4.153 

2% 

23 

3%   . 

±K 

4.255 

m 

21 

EEMARKS.  —  As 

upsetting    reduces    the    strength  of  iron,  bars 

having  the  same  diameter  at 

root  of  thread  as  that  of  the  bar,  in- 

variably  break  in  the  screw  end,  when  tested  to  destruction,  without 

developing  the  full  strength  of  the  bar.     It  is  therefore  necessary  to 
make  up  for  this  loss  in  strength  by  an  excess  of  metal  in  the  upset 

screw  ends  over  that 

in  the  b 

ar. 

The  above  table  ii 

!  the  ree 

tilt  of  numerous  tests  on  finished  bars 

made  at  the  Keystone  Bridge  Company's  Works  in  Pittsburgh,  and  gives 
proportions  that  will  cause  the  bar  to  break  in  the  body  in  preference 

to  the  upset  end. 

The  screw  threads  in  above  table  are  the  Franklin  Institute  standard. 

To  make  one  upset  end  for  5"  length  of  thread  allow  6"  length  of 

rod  additional. 

197                                                              4 

STANDARD  SCREW  THREADS,  NUTS  AND 
BOLT  HEADS.—  Recommended  by  the  Franklin  Institute. 

SCREW   THREADS. 

Nuts  and  Bolt  Heads 

A?/        ^      ^       ,m 

are   determined   by  the  fol- 

/^ll^a    £.0  /^ll^    o  j    //|l||k. 

lowing  rules,  which  apply  to 

"                        ^  /^HlK. 

Square  and  Hexagon    Nuts 

both  : 

^^^^^^J^^^^^^^^^^^^^^^^^^^^ 

Short  diameter  of  rough  nut 

Angle  of  Thread  60°.  Flat  at  Top  and  Bottom^  %  of  pitch. 

=  IJ^  x  dia,  of  bolt  -  y3  in. 

Dia.  of 

Dia.  at  Root       Threads 

Short  diameterof  finished  nut 

Screw. 

of  Thread.        per  Inch. 

=  V£  :<  dia.  of  bolt  +  1-18  in. 

Inches. 

Inches.              No. 

Thickness  of  rough  nut 

i/ 

.185            20 

=  diameter  of  bolt. 

5 

.240            18 

Thickness  of  finished  nut 

% 

.294            16 

=  diameter  of  bolt  —  1-16  in. 

T^ff 

.344 

14 

Short  diameter  of  rough  head 

y 

.400 

13 

=  1^  X  dia.  of  bolt  -f  %in. 

^ 

.454 

12 

Short  dia.  of  finished  head 

%, 

.507 

11 

=1%  x  dia.  of  bolt  -  1-16  in. 

% 

.620 

10 

Thickness  of  rough  head 

% 

.731 

9 

=  y2  short  dia.  of  head. 

I 

.837 

8 

Thickness  of  finished  head 

.940 

7 

=  dia.  of  bolt  —  1-16  in. 

1% 

1.065 

7 

The    long   diameter   of    a 

1% 

1.160 

6 

hexagon  nut  may  be  obtained 

\y 

1.284 

6 

by    multiplying    the     short 

\y 

1.389 

diameter   by  1.155,  and   the 

1  3/ 

1.490 

5 

long   diameter  of  a   square 

10 

1.615 

5 

nut  by  multiplying  the  short 

2 

1.712 

diameter  by  1.414. 

1.962 

4  1/ 

The   above   standards    for 

23^ 

2.175 

4/2 

screw  threads,  nuts  and  bolt 

fc>/2 

2.425 

4 

heads,  were  recommended  by 

/4 

the    Franklin    Institute    in 

3 

2.629 

aorrrk 

3K 

Dec.  1864.    The  standard  for 

3/^ 

.879 

31  r\/\ 

3/2 

screw  threads  has  been  very 

i| 

.100 

3.317 

34 

generally    adopted    in     the 
United  States,  but  the  pro- 

4 

3.567 

3 

portions    recommended    for 

4M 

3.798 

2¥ 

nuts  and  bolt  heads  have  not 

4f^ 

4.028 

found  general  acceptance  be- 

4% 

4.255 

*& 

cause  of  the  odd  sizes  of  bar 

5                4.480 

2>£ 

—  not  usually  rolled  by  the 

5^            4.730 

2M 

mills  —  which  they  would  re- 

5K            5.053 

m 

quire   from  which   to  make 

5%             5.203 

the  nut. 

.        6           !     5.423              2MX 

£ 

WHITWORTH'S    STANDARD    ANGULAR 
SCREW    THREADS. 


Angle  of  Thread  55°. 

Depth  of  Thread  =  pitch  of 
screw. 

Y&  of  depth  is  rounded  off  at 
to  and  bottom. 


p 

Number  of  threads  to  the 
inch  in  square  threads  =  ^  the  "number  in  angular  threads. 


Dia,  of    ;    Threads 
Screw,     to  the  Inch. 
In.             No. 

Dia.  of 
Screw. 
In. 

Threads 
to  the  Inch. 
No. 

Dia.  of 

Screw. 
In. 

Threads 
to  the  Inch. 
No. 

Dia.  of 
Screw. 
In. 

Threads 
to  the  Inch. 
No. 

1-4              20 

1 

8 

2 

4  1-2 

4 

3 

5-16     i        18 

1  1-8 

7 

2  1-4 

4 

4  1-4 

2  7-8 

3-8              16 

1  1-4 

7 

2  1-2 

4 

4  1-2 

2  7-8 

7-16     :        14 

1  3-8 

6 

23-4 

3  1-2 

4  3-4 

2  3-4 

| 

1-2       i        12 

11-2 

6 

3 

3  1-2 

5 

2  3-4 

5-8              11 

1  5-8 

5 

3  1-4 

3  1-4 

5  1-4 

2  5-8 

3-4              10 

1  3-4 

5 

3  1-2 

3  1-4 

5  1-2 

2  5-8 

7-8                9 

1  7-8 

4  1-2 

3  3-4 

3 

5  3-4 

2  1-2 

6 

2  1-2 

WOOD    SCREWS. 

Diameter  =  number  X  0.01325  -f  0.056. 


No. 

Dia. 

No. 

Dia. 

No. 

Dia. 

No. 

Dia. 

No. 

Dia. 

0 

1 
2 
3 
4 
5 

.056 
.069 
.082 
.096 
.109 
.122 

6 
7 
8 
9 
10 
11 

.135 
.149 
.162 
.175 
.188 
.201 

12 
13 

11 

16 

17 

.215 
.228 
.241 
.255 
.268 
.281 

18 
19 
20 
21 
22 
23 

.293 
.308 
.321 
.334 
.347 
.361 

24 
25 
26 
27 
28 
29 
30 

.374 
.387 
.401 
414 

.427 
.440 
.453 

TACKS. 


Title. 
fe 

Length. 
In. 

No., 
per  Ib. 

Title. 
Oz. 

Length. 
In. 

No. 
perlb. 

Title. 
Oz. 

Length. 
In. 

No. 
perlb. 

Title. 
Oz. 

Length. 
In. 

No. 
perlb. 

i 
1  1-2 
2 
21-2 

1-8 
3-16 
1-4 
5-16 

16000 
10666 
8000 
6400 

3 

4 
6 
8 

3-8 

7-16 
9-16 
5-8 

5333 
4000 
2666 
2000 

10 
12 
14 

16 

11-16 
3-4 
13-16 
7-8 

1600 
1333 
1143 
1000 

18 
20 
22 
24 

15-16 
1  -• 
1  1-16 
1  1-8 

888 
800 
727 
666 

WROUGHT    SPIKES. 

Number  to  a  keg  of  150  Ibs. 


In. 


/  in. 

No. 


3  2250 

3  1-2  1890 

4  i  1650 

4  1-2  1464 

5  1380 

6  1292 


n. 

o. 


1135 
1064 


742 
570 


Length. 
In. 


v- 


1161 


in. 


635 
573 


455 
424 
391 


445 

384 


270 
249 


256 
240 
322 


129 


?  r. 

SIZES  AND  WEIGHTS   OF   HOT  PRESSED 

SQUARE   NUTS. 

As  manufactured  by  Charles  &  McMurtry,  Pittsburgh,  Pa.    The  sizes  are  the  usual  manufacturers', 
not  the  Franklin  Institute  Standard.    Both  weights  and  sizes  are  for  the  unfinished  Nut. 

Size  of     1    Weight  of        Rough 

Thickness       Side  of        n:  i    1  No.  of  Nuts  in 

Bolt.      1     One  Nut.           Hole. 

of  Nut. 

Square.                               100  Ibs.    . 

K           -014 

.7 

H 

K 

.71 

6900 

A 
H 

.029 
.048 

ft 

Ps 

1 

.88 
1.06 

3450 
2080 

A 

.078 

H 

_7_ 

K        1.24 

1280 

P 

.088 

& 

y* 

1.24      1140 

.116         TV 

% 

1            1.41 

860 

1 

_9 

.161 

% 

i 

IK 

1.59 

620 

y% 

.172 

9 

% 

1/8 

1.59 

580 

H 

.22 

ft 

% 

ik 

1.77 

460 

%. 

.31 

H 

% 

IX 

1.94 

320 

% 

.38 

f  1 

H 

2.12 

260 

i/ 

.56 

If 

IM 

2.30 

180 

% 

.63 

If 

H 

IX 

2.47 

160 

1 

.69 

% 

i 

IK 

2.47 

144 

l 

.91 

Js 

i 

2 

2.83 

110 

IK 

1.00 

It 

l/'S 

2 

2.83 

100 

1.43 

it 

1)1 

2^ 

3.18 

70 

1& 

1.54 

lyV 

IK 

2^ 

3.18 

65 

lx^ 

1.79 

ly1^ 

IK 

2/^ 

3.54 

56 

1>8 

2.4 

I* 

2^    . 

3.89 

42 

IK 

3.1 

1ft 

'i1^ 

3 

4.24 

32 

4.0 

ift 

i|S 

31^ 

4.60 

25 

i| 

5.0 
5.9 

iii 

LP 

ii 

4.95 
5.30 

20 
17 

2 

7.1, 

iff 

2 

4 

5.66 

14. 

7.4 

1% 

4 

5.66 

13.5 

2^ 

8.1 

2 

2^ 

4^ 

6.01 

12.3 

2% 

8.3 

2K 

2% 

41^ 

6.01 

12.0 

2yz     10.9 

2/2 

2/^ 

4^ 

6.36 

9.14 

2%       13.2 

2TV 

2^ 

4^ 

6.72 

7.55 

3          14.9 

aj| 

3 

5 

7.07 

6.72 

3^     !  17.5 

31^ 

5j^ 

7.78 

5.70 

:  SK-.  121.1 

3/8 

3K         6 

8.49 

4.75. 

iS                                                                                                         ' 

SIZES   AND   WEIGHTS   OP   HOT   PRESSED 
HEXAGON   NUTS. 

As  manufactured  by  Charles  &  McMurtry,  Pittsburgh,  Pa.    The  sizes  are  the  visual  manufacturers', 
net  the  Franklin  Institute  Standard.    Both  weights  and  sizes  are  for  the  unfinished  Nut. 


M  Size  of 
*    Belt. 

Weight  of 
One  Nut. 

Rough        Thickness 
Hole.           of  Nut. 

Short 
Diameter. 

Long 
Diameter. 

No.  of  Nuts  in 
100  Ibs. 

~77 

.013 

,', 

H 

I./ 

.58 

8000 

A 

.026 

"K 

A 

^ 

.72 

3840 

3> 

.042 

M 

K 

.87 

2400 

A 

.071 

P 

TV 

% 

1.01 

1400 

I/ 

.069 

& 

1  / 

Js 

1.01 

1440 

k 

.100 

M 

1 

1.15 

1000 

A 

.161 

}l 

A 

iNf 

1.30 

620 

M 

.147 

9 

^ 

1?8     ' 

1.30 

680 

/N} 

.200 

T9G 

M 

1'4 

1.44         500 

5/ 

ts& 

li 

y 

lx^ 

1.44 

53© 

7 

'•23 

% 

.26 

f? 

34 

1^8 

1.59 

380 

3/ 

.33 

% 

11^ 

1.73 

300 

7X 

.45 

J5/ 

1.88 

220 

% 

.53 

25 

3  2 

i  , 

1M 

1.88 

190 

1 

.59 

J« 

i 

IK 

2.02 

170 

1 

.63 

]_?8 

2.02 

160 

1L3 

.95 

it 

1M 

2/4 

2.31 

105 

l1^ 

1.43 

IT  a 

1^8 

2^ 

2.60 

70 

13/ 

1.64 

JJL 

l1^ 

2^ 

2.89 

61 

1& 

2.4 

1& 

1M 

2% 

3.18 

42 

158 

3.0 

i'A 

IK 

3 

3.46 

33 

1/4 

3,7 

1A  • 

1/8 

3M 

3.75 

27 

U-8 

4.8 

IT! 

2 

4.04 

21 

2 

4.5 

Iff 

2 

31  / 

4.04^ 

22 

5.1 

1% 

3/1 

4.33* 

19.5 

2>4 

5.4           2 

2K 

3% 

4.33 

18.4 

23« 

6.3           2^ 

2% 

4 

4.62 

15.84 

2'4         7.6           2K' 

414 

4.91 

13.11 

2%     ,    9.3           2^ 

2^, 

4)^ 

5.20 

10.80 

3          11.8 

2|-i 

3 

4% 

5.48 

8.46 

3*4       15.9 

2tf 

31^ 

5 

5.77 

6.30 

3!<C       23.8 

3^' 

3K 

51^ 

6.06 

4.20 

131 


xxx^? 

IN-OOOO-^^^-iT-iT-iT-^OGOOOOOOOOOOOOOOOOOOOO 
CV}  ,_  ,-H  ,_,,_,     ,_  ,-H  .^H  „_ 


5  O2  1O  OS    OO  OO  ^>  CC  OO 
T— IT— IT-"     GvJCOlOCOJN- 


'^•is.aS,   .looc^-co 
=^§^'a?"-;iO«o 

" C ,g  \£ "** ^ 


«££  ,3o^>r-<»ce^ao«}t-o»,-«|:*io  ^gg^ogg 


<^  -T}<  |>- -^f  lO    T-<  CO          Is- IN-  CO 

^  10  co  oq  <o  co  co>os  cooq»o<oio     <io 

' 


EXPLANATION    OF    TABLES    ON    RIVETS 
AND    PINS. 

Pages    135   to   137,  inclusive. 

In  transmitting  stress  by  means  of  rivets,  it  is  customary  to 
disregard  the  friction  between  the  parts  joined,  as  too  uncertain 
an  element  to  be  relied  upon  to  any  extent.  The  rivets  must 
then  be  proportioned  for  the  entire  stress  which  is  to  be  trans- 
mitted from  one  plate,  or  group  of  plates,  to  the  other,  and  they 
must  be  of  sufficient  size  and  number,  to  present  ample  resistance 
to  shearing  and  afford  sufficient  bearing  area,  so  as  not  to  cause  a 
crushing  of  the  metal  at-  the  rivet  holes.  This  latter  condition, 
while  generally  observed  for  pins,  is  very  often  entirely  over- 
looked in  riveted  work.  Its  observance,  in  most  cases  of 
riveted  girders  with  single  webs,  determines  the  size  and  number 
of  rivets  to  be  used,  and  frequently  makes  it  necessary  to  adopt  a 
greater  thickness  of  web  than  would  otherwise  be  required. 
Thus,  if  the  web  is  -f^"  thick,  the  rivets  connecting  the  same 
with  the  flange  angles  have  a  bearing  value  of  only  3520  Ibs. 
for  a  %"  rivet, .while  their  shearing  value  is  =  2  X  3310  = 
6620  Ibs.  per  rivet,  the  rivets  being  in  double  shear.  Con- 
sequently, while  the  usual  thickness  of  web  of  floorbeams  for 
railway  bridges  is  ffif,  it  sometimes  becomes  necessary,  for 
shallow  floorbeams,  to  increase  this  thickness  to  )4ff  and  even 
$£rf,  in  order  that  the  pressure  of  the  rivets  upon  the  semi-intrados 
of  the  rivet  holes  be  not  excessive,  between  the  points  of  support 
of  floorbeam  and  of  application  of  the  load,  (in  which  space  the 
transmission  of  stress  from  web  19  flanges  takes  place.) 

The  pressure  usually  allowed  upon  rivet-bearing  is  15000  Ibs. 
per  square  inch,  as  assumed  in  table,  the  bearing  area  being  the 
diameter  of  hole  multiplied  by  the  thickness  of  metal.  This 

'"  133 


pressure  is  somewhat  greater  than  is  generally  allowed  for  pins, 
in  consideration  of  the  neglect  of  the  friction  between  plates 
in  riveted  work. 

Pins  must  be  calculated  for  shearing,  bending  and  bearing 
stresses,  but  one  of  the  latter  two  only,  in  almost  every  case, 
determines  the  size  to  be  used.  The  stress  allowed  upon  pin- 
bearing  in  bridges  proportioned  to  a  factor  of  safety  of  five, 
is  usually  12500  Ibs.,  and  the  maximum  fiber  strain  by  bending, 
15000  Ibs.  per  square  inch.  Where  groups  of  bars  are  connected 
to  the  same  pin,  as  in  the  lower  chords  of  truss  bridges,  the  size 
of  bars  must  be  so  chosen  and  the  bars  so  placed  that  at  no 
point  on  the  pin  will  there  be  an  excessive  bending  strain,  on  the 
presumption  that  all  the  bars  are  strained  equally  per  square  inch. 

The  following  examples  will  illustrate  the  use  of  the  tables  -. 

A  pin  in  the  bolster  or  end  shoe  of  a  bridge  has  to  carry  a 
load  of  40000  Ibs.  between  two  points  of  support;  what  size 
of  pin  is  required,  presuming  the  distance  between  points  (i.  e., 
centers)  of  support  of  bolster  plates  and  centers  of  pressure  of 
end  post  plates  =  2>£"? 

Anstver  :  Bending  moment  =  20000  Ibs.  x  2>£  ==  50000  inch 
Ibs.,  therefore  %%»  pin  required  for  15000  Ibs.  fiber  strain,  since 
the  allowed  moment  for  3>("  =  50600,  as  per  table. 

Required  the  thickness  of  metal  in  the  top  chord  or  in  a  post 
of  a  bridge,  that  will  give  sufficient  bearing  area  to  a  3^;/  pin, 
having  to  transmit  a  stress  of  63300  Ibs.,  the  allowed  pressure  per 
square  inch  on  bearing  being  12500  Ibs.  maximum. 

The  bearing  value  of  a  3^/x  pin  for  \"  thickness  of  plate  = 
42200  Ibs.,  therefore  the  thickness  of  metal  required 


l/^'j  °r  each  of  the  two  plates  in  the  chord  or  post  will  have  to 
be      "  thick. 


134 


o   ; 


«       -3 


ooo 


t>CO 
CO-^ 


IOI>  (M 

(MOO       lOi-H 


10 
(M 


10 


(MOO       lOi-H       C^CO  CD       (MOO 

COCO       l>00       0005       OO       rHiH 


135 


MAXIMUM  BENDING  MOMENTS  TO  BE  AL- 
LOWED ON  PINS  TOR  MAXIMUM  FIBER 
STRAINS  OF  15000,  20000  AND  22500  LBS. 
PER  SQUARE  INCH. 


Diam. 
of 
Pin. 
Inches. 

Moment 
for 
8  =  15000. 
Lbs.  in. 

Moment 
for 
S  =  20000. 
Lbs.  in. 

Moment 
for 
S  =  22500. 
Lbs.  in. 

Diam. 
of 

Pin. 
Inches. 

Moment  1  Moment    Moment 
for       for      for 
S  =  15000.  S  =  20000.  S  =  22500. 
Lbs.  in.  j  Lbs.  in.    Lbs.  in. 

1 

1470   1960 

2210 

4 

94200  125700  14140O 

1¥ 

2100   2800 

3140 

4M 

103400  137800  155000 

1# 

2880   3830 

4310 

414  H13000  150700  169600 

IK 

3830   5100 

5740 

4% 

123300  164400  18500O 

IX 

4970   663O 

7460 

4* 

134200  178900  201300 

1% 

6320   8430 

9480 

4*£ 

14570O  194300  21850O 

i% 

7890  10500 

11800 

4% 

157800  21O400  23670O 

i% 

9710  12900 

14600 

4^ 

170600  227500  255900 

2 

11800  15700 

17700 

5 

184100  245400  276100 

2# 

14100  18800 

21200 

5M 

198200  264300  29730O 

2^ 

16800  2240O 

25200 

5# 

213100  284100  319600 

2% 

19700  26300 

29600 

5% 

228700  304900  34300O 

2# 

23000  30700 

34500 

&x 

245000  326700  367500 

2% 

26600 

35500 

40000 

5% 

262100  349500  39310O 

2M 

30600 

40800 

45900 

5% 

280000  373300  419900 

2% 

35000 

46700 

52500 

5% 

2986OO  398200  44790O 

3 

39800 

53000 

59600 

6 

318100  424100  477100 

3^ 

44900 

59900 

67400 

8M 

338400  451200  507600 

3^ 

50600 

67400 

75800 

8£ 

3595OO  479400  53930O 

3% 

56600 

75500 

84900 

6% 

381500  5087OO  572300 

33^ 

63100  84200 

94700 

Q1A 

404400  539200  606600 

3% 

70100  93500 

105200 

6% 

428200  57090O  64230O 

3M 

77700  103500 

116500 

6M 

452900  603900  679400 

3% 

85700114200128500 

m 

478500  638000  71780O 

REMARKS — The  following  is  the  formula  for  flexure  applied  to  pins: 


M=  moment  of  forces  for  any  section  of  the  pin.  % 

S  =  strain  per  sq.  in.  in  extreme  fibers  of  pin  at  that  section. 
A=area  of  section. 
d= diameter. 
7T=3.14159. 

The  forces  are  assumed  to  act  in  a  plane  passing  through  the  axis 
of  the  pin. 

The  above  table  gives  the  values  of  M  for  different  diameters  of  pin, 
and  for  three  values  of  S. 

If  M  max.  is  known,  an  inspection  of  the  table  will  therefore  show 
what  diameter  of  pin  must  be  used,  in  order  that  <S  does  not  exceed 
15000,  20000  or  22500  Ibs.,  as  the  requirements  of  the  case  may  be. 

For  Railroad  Bridges  proportioned  to  a  factor  of  safety  of  5,  it  is 
customary  to  make  S  max.  =  1500Q  Ibs.  in  iron  and=  20000  Ibs.  in  steel. 

136 


BEARING  VALUE  OF  PINS  FOR  ONE  INCH 
THICKNESS    OF   PLATE. 

(—  Dia.  of  Pin  X  1"  X  strain  per  sq.  inch.) 

Diameter  of 
Pin. 

Inches. 

1 

IX 

$ 

1# 

Area  of            Bearing  Value  at       Bearing  Value  at 
Piu>                  12500  Ibs.               15000  Ibs. 
square  In'ches.          per  square  inch.    ;    per  square  inch. 
Lbs.                                 Lbs. 

.785 
.994 
1.227 
1.485 
1.767 

12500 
14100 
15600 
17200 
18800 

15000 
16900 
18800 
20600 
22500 

!5/8 

i 

2 

2.074 
2.405 
2.761 
3.142       | 

20300 
21900 
23400 
25000 

24400 
26300 
28100 
30000 

2# 

2M 
2& 
2# 

3.547 
3.976 
4.430 
4.909 

26600 
28100 
29700 
31300 

31900 
33800 
35600 
37500 

2^ 
2% 
2% 
3 

5.412 
5.940 
6.492 
7.069 

32800 
34400 
35900 
37500 

39400 
41300 
43100 
45000 

3'  8' 

3% 
3% 
3J8X 

7.670 
8.946 
10.32 
11.79 

39100 
42200 
45300 
48400 

46900 
50600 
54400 
58100 

418 

m 

m 
•  478x 

13.36 
15.03 
16.80 
18.67 

51600 
54700 
57800 
60900 

61900 
65600 
69400 
7310O 

5M 

m 

5H 

SH 

20.63 
22.69 
24.85 
27.11 

64100 
67200 
70300 
73400 

78900 
80600 
84400 
88100 

8?BX 

6M 
6% 

6.7'8 

29.46 
31.92 
34.47 
37.12 

76600                   91900 
79700                   95600 
82800                   99400 
85900                 103100 

«  —  £ 

—  « 

WOODEN    BEAMS. 

Safe  Load,  Uniformly  Distributed,  for  Rectangular 

White  or  Yellow  Pine  Beams  one  inch  thick, 

allowing  1200  Ibs.  per  square 

inch  fiber  strain. 

To  obtain  the  safe  load  for 

any  thickness,  multiply  the 

safe 

load  given  in  table,  by  the  thickness  of  beam. 

To  obtain  the  required  thickness  for  any  load,  divide  by  the 

safe  load  for  1  inch,  given  in  table. 

a 
"*  -^s 

DEPTH   OF   BEAM. 

„ 

6" 

7// 

8"     9" 

10" 

11" 

12" 

13" 

14// 

15" 

16" 

Feet. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

5 

960 

1310  1710  2160 

2670 

3230 

3840 

4510 

5230 

6000 

6830 

6 

800 

1090  1420 

1800 

2220 

2690 

3200 

3760 

4360 

5000 

5690 

7 

690 

930 

1220  1540 

1900 

2300 

2740 

'3220 

3730 

4290 

4880 

8 

600 

820 

1070   1350 

1670 

2020 

2400 

2820  3270 

3750 

4270 

9 

530 

730 

950 

1200 

1480 

1790 

2130 

2500  2900 

3330 

3790 

10 

480 

650 

850 

1080 

1330 

1610 

1920 

2250 

2610 

3000 

3410 

11 

440 

590 

780 

980 

1210 

1470  j  1750 

2050  2380 

2730 

3100 

12 

400     540 

710 

900 

1110 

1340  1600 

1880 

2180 

2500 

2840 

13 

370     500 

660 

830 

1030 

1240 

1480 

1730 

2010 

2310 

2630 

14 

340 

470 

610 

770 

950 

1150 

1370 

1610 

1870 

2140 

2440 

15 

320 

440 

570 

720 

890 

1080 

1280 

1500 

1740 

2000 

2280 

16 

300 

410 

530 

680 

830 

1010 

1200 

1410 

1630 

1880 

2130 

17 

280 

380 

500 

640 

780 

950 

1130 

1330 

1540 

1760 

2010 

18 

270 

360 

470 

600 

740 

900 

1070 

1250 

1450 

1670 

1900 

19 

250 

340 

450 

570 

700 

850 

1010 

1190  1  1380 

1580 

1800 

20 

240 

330 

430 

540 

670 

810 

960 

1130 

1310 

1500 

1710 

21 

230 

310 

410 

510 

630 

770 

910 

1070 

1240 

1430 

1630 

22 

220 

300 

390 

490 

610 

730 

870 

1020 

1190 

1360 

1550 

23 

210 

280 

370     470 

580 

700 

830 

980  1140 

1300 

1480 

24 

200     270 

360  ;  450 

560 

670 

800 

940   1090 

1250 

1420 

25' 

190 

260 

340 

430 

530 

650    770 

900 

1050 

1200 

1370 

26 

180 

250 

330 

420 

510 

620     740 

870 

1010 

1150 

1310 

27 

180'  240 

320 

400 

500 

600     710 

830 

970 

1110 

1260 

28 

170!  230 

300 

390 

480 

580     690 

800 

930 

1070 

1220 

29 

1701  230 

390 

370 

460 

560     660 

780 

900 

1030 

1180 

'4  

Si 

EXPLANATION  OF  TABLES  ON  MAXIMUM 
STRESSES  IN  PRATT  AND  WHIPPLE 

TRUSSES. 
Pages  141  to  143,  inclusive. 

These  tables  give  the  stress  in  each  member  of  a  Pratt  (single 
quadrangular)  or  Whipple  (double  quadrangular)  truss,  for  any 
number  of  panels  not  exceeding  twelve  in  the  former,  and  twenty 
in  the  latter  case,  on  the  assumption  that  the  load  is  uniform  per 
foot,  and  the  panels  are  all  of  the  same  length.  The  stresses  are 
given  in  terms  of  the  truss-panel  dead  and  moving  loads,  repre- 
sented respectively  by  W  and  L.  These  are  obtained  by  multi- 
plying the  dead  load  per  foot  of  bridge,  in  the  case  of  W,  and 
the  moving  or  live  load  per  foot  of  bridge,  in  the  case  of  L,  by 
half  the  panel  length. 

The  letters  W  and  L  are  placed  at  the  top  of  column,  in  tables, 
and  not  next  to  the  figures  to  which  they  belong,  for  want  of  space. 
The  stress  in  aB,  for  example,  in  a  twelve  panel  Pratt  truss, 
=  5.5  W  X  5.5  L,  and  in  Be  =  4.5  W  X  f  |  L,  both  multi- 
plied by  the  quotient  specified  in  the  last  column. 

The  system  of  lettering  employed  is  shown  by  Figs.  7  and  8, 
on  page  26  of  the  lithographs,  and,  it  is  believed,  is  the  best  in 
use.  By  making  a  sketch  of  the  truss  under  consideration  and 
lettering  the  vertices  in  the  manner  shown,  the  truss  members  to 
which  reference  is  had  in  the  tables,  can  be  readily  identified. 

In  the  following  tables,  "the  dead  load  is  assumed  as  concen- 
trated at  the  lower  vertices  of  the  trusses,  for  through  bridges, 
and  at  the  upper  vertices,  for  deck  bridges.  For  through  bridges 
of  very  large  span,  the  stresses  thus  obtained  for  the  posts  must 
be  increased  by  the  truss-panel  weight  of  the  upper  portion  of 
the  truss,  including  the  lateral  bracing;  but  in  small  spans,  the 
increase  of  stress  on  this  account  is  so  inconsiderable  that  it  is 
usually  neglected. 

Note :  In  order  to  calculate  the  stresses  in  a  Whipple  or  double 
quadrangular  truss  by  statical  methods,  it  is  necessary  to  consider 
the  truss  as  the  combination  of  two  Pratt  trusses  or  single  systems 
of  bracing,  and  assume  that  each  of  these  two  systems  is  strained 
in  the  same  manner  as  if  one  were  independent  of  the  other.  If 
the  number  of  panels  is  odd,  each  of  the  two  systems  is  unsym- 


metrical,  which  has  the  effect  of  making  the  stress  in  the  middle 
panel  of  the  lower  chord  slightly  smaller  than  the  stress  in  the 
corresponding  panel  of  the  top  chord.  To  avoid  this  peculiarity 
and  obtain  equal  stresses  in  these  members,  a  division  into  sym- 
metrical systems  is  sometimes  assumed  for  the  dead  load  stresses 
and  for  the  full  load,  by  considering  the  counter  ties  canceled.  For 
the  live  load  stresses  obtained  by  partial  loading,  however,  it  is 
again  necessary  to  divide  into  unsymmetrical  systems,  so  that, 
while  there  appears  to  be  no  good  reason  in  favor  of  this  method, 
it  has  the  objection  of  inconsistency.  The  difference  in  the 
resulting  stresses  obtained  by  the  two  methods  is  so  small  as  not 
to  be  of  practical  consequence.  Each  of  the  two  systems  is 
assumed  to  carry  one-half  of  the  panel  load  at  the  top  of  the 
inclined  end  posts. 

ILLUSTRATION  OF  APPLICATION  OF  TABLES,  ALSO 

OF  THE  USE  OF  TABLE  OF  NATURAL  SINES, 

TANGENTS  AND   SECANTS. 

A  Pratt  truss  of  135'  span  and  18'  depth,  is  divided  into  nine 
panels  of  15'  each.  Required  the  stress  in  first  main  tie  Be,  and 
in  middle  panel  DE  of  top  chord,  for  a  dead  load  of  1200  Ibs. 
and  a  moving  load  of  3000  Ibs.  per  lineal  foot  of  bridge. 

1900 
W  =  ~-  x  .15  =  9000  Ibs. 


-^°i  x   15  =  22500  Ibs. 


Q  /     />  -IO 

DE=(10W  +  10  L)-j|- 

The  factor  -^r- ,  or  panel  length  divided  by  depth  of  truss,  is 
lo 

the  tangent  of  the  angle,  for  which  the  length  Be,  divided  by 
depth  of  truss,  is  the  secant.     By  table  of  natural  sines,  tangents 

and  secants,  for  tangent  =  -—  =  0.833,  the   secant  =  1.302; 
lo 

therefore 

Be  ==  97000  X  1.30  =  126100  Ibs. 

DE  =  315000  X  -j|~  =  262500  Ibs. 
140 


:5— 
MAXIMUM   STRESSES    UNDER 

DEAD 

AND 

MOVING  LOADS  IN  PRATT  OR  SINGLE 

QUADRANGULAR   TRUSSES 

With  inclined  end  posts  and  equal  panel 

3,  for  Through  and  Deck  Bridges. 

W  =  deac 

1  load  and  L  =  moving  load  per  truss  and  per  panel. 

Member. 

12  Panel     11  Panel 
Truss.          Truss. 

10  Panel 

Truss. 

9  Panel     8  Panel 
Truss.    ,     Truss. 

Multi- 
ply by: 

W+L         W+L 

W+L 

W+L        W+L 

aB 

5.5+5.5        5+5 

4.5+4.5 

4_1_4       3.5+3.5 

1 

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'3 

MAXIMUM    STRESSES    UNDER   DEAD   AND 

MOVING 

LOADS   IN   WHIPPLE   OR 

DOUBLE   QUADRANGULAR 

TRUSSES 

With  inclined  end  posts 

and  equal  pane 

.s,  for  Through  and  Deck  Bridges. 

W  =  dead  load  and  L  =  moving 

ioad  per  truss  and  per  panel. 

TUT          1. 

20  Panel 

19  Panel 

18  Panel  !  17  Panel 

16  Panel 

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Truss. 

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—  ; 

MAXIMUM    STRESSES   UNDER   DEAD    AND 

MOVING  LOADS  IN  WHIPPLE   OR 

DOUBLE   QUADRANGULAR 

TRUSSES 

With  inclined  end  posts  and  equal  panels,  for  Through  and  Deck  Bridges. 
W  =  dead  load  and  L  =  moving  load  per  truss  and  per  panel. 


Member. 


15  Panel 
Truss. 


W+L 


14  Panel 
Truss. 


W+L         W+L 


6.5+6.5 


2.0+^! 
1.5+2 
1.0+ 
0.5+1 
0.0+ J 


7+7 
W+W 

W+W 

W+W 
;V¥+¥^3 


6.5+  6.5     6+6 
9.5+  9.5;  W+W 

14.5+14.5  n  *° 

18.5+18.5 

21.5+21.5 

23.5+23.5,  „   ,    „ 

24.5+24.5!  W+2TV 
~    -       ~~=FG 


4.24.5    It5  i 


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—  2^5     1.0+1 

__^s  0.5+1 
--W  o.o- 

-r4T+4-f  -0.5+-' 


143 


+-W1 


NATURAL  SINES 

—  £ 
,  TANGENTS  AND  SECANTS  , 

Advancing  by  1O  min. 

Beg. 
0 

Min. 

00 
10 
20 

Sine.     Tangent. 

Secant. 

Deg. 

Min. 

Sine. 

Tangent.  !  Secant. 

!  4 

.0000      .0000 
.0029      .0029 
.0058      .0058 

1.0000 
1.0000 
1.0000 

5 

00     .0872 
10      .0901 
20      .0929 

.0875 
.0904 
.0934 

1.0038 
1.0041 
1.0043 

30 
4fc 
50 

.0087      .0087 
.0116      .0116 
.0145      .0145 

1.0000 
1.0001 
1.0001 

30 
40 
50 

;0958 
.0987 
.1016 

.0963 
.0992 
.1022 

1.0046 
1.0049 
1.0052 

1 

00 
10 
20 

.0175      .0175 
.0204      .0204 
.0233      .0233 

1.0002 
1.0002 
1.0003 

6 

00 
10 
20 

.1045 
.1074 
.1103 

.1051 
.1080 
.1110 

1.0055 
1.0058 
1.0061 

30 
40 
50 

.0262      .0262 
.0291      .0291 
.0320      .0320 

1.0003 
1.0004 
1.0005 

30 

40 
50 

.1132 
.1161 
.1190 

.1139 
.1169 
.1198 

1.0065 
1.0068 
1.0072 

2 

00 
10 
20 

.0349      .0349 
.0378  i    .0378 
.0407  |    .0407 

1.0006 
1.0007 
1.0008 

7 

00 
10 
20 

.1219 

.1248 
.1276 

.1228 
.1257 
.1287 

1.0075 
1.0079 
1.0082 

30 
40 
50 

.0436      .0437 
.0465      .0466 
.0494      .0495 

1.0010 
1.0011- 
1.0012 

30 
40 
50 

.1305 
.1334 
.1363 

.1317 
.1346 
.1376 

1.0086 
1.0090 
1.0094 

3 

00 
10 
20 

.0523      .0524 
.0552      .0553 
.0581      .0582 

1.0014 
1.0015 
1.0017 

8 

00 
10 
20 

.1392 
.1421 
.1449 

.1405 
.1435 
.1465 

1.0098 
1.0102 
1.0107 

30 
40 
50 

.0610      .0612 
.0640      .0641 
.0669      .0670 

1.0019 
1.0021 
1.0022 

30 
40 
50 

.1478 
.1507 
.1536 

.1495 
.1524 
.1554 

1.0111 
1.0116 
1.0120 

4  :  00  '    .0698      .0699 
;  10  ;    .0727      .0729 
|  20     .0756      .0758 

1.0024 
1.0027 
1.0029 

9     00 

10 
20 

.1564 
.1593 
.1622 

.1584 
.1614 
.1644 

1.0125 
1.0129 
1.0134 

30     .0785      .0787 
40  i    .0814      .0816 
|  50  i    .0843      .0846 

ft.     -1      '  

1.0031 
1.0033 
1.0036 

30 
1  40 
50 

.1650  I    .1673  1  1.0139 
.1679  i    .1703    1.0144 
.1708  i    .1733    1.0149 

> 

NATURAL  SINES,  TANGENTS  AND  SECANTS. 

Min.     Sine. 

(CONTINUED.) 

Deg. 
10 

Tangent.  Secant. 

Deg.  Min. 

Sine. 

Tangent.  Secant. 

00     .1736 
10     .1765 
20     .1794 

.1763    1.0154 
.1793    1.0160 
.1823    1.0165 

15 

00 
10 
20 

.2588      .2679    1.0353 
.2616      .2711     1.0361 
.2644      .2742    1.0369 

i  30     .1822 
!  40     .1851 
;  50     .1880 

.1853    1.0170 
.1883    1.0176 
.1914    1.0181 

30 
40 
50 

.2672  !    .2773    1.0377 
.2700      .2805    1.0386 
.2728      .2836    1.0394 

11 

00     .1908 
10      .1937 
20     .1965 

.1944    1.0187 
.1974    1.0193 
.2004    1.0199 

16 

00 
10 
20 

.2756 
.2784 
.2812 

.2867    1.0403 
.2899  :  1.0412 
.2931     1.0421 

* 

30      .1994 
40      .2022 
50      .2051 

.2035    1.0205 
.2065    1.0211 
.2095    1.0217 

30 
40 
50 

.2840 
.2868 
.2896 

.2962 
.2994 
.3026 

1.0429 
1.0439 
1.0448 

12 

00      .2079 
10      .2108 
20      .2136 

.2126    1.0223 
.2156    1.0230 
.2186    1.0236 

17 

00 
10 
20 

.2924 
.2952 
.2979 

.3057 
.3089 
.3121 

1.0457 
1.0466 
1.0476 

30      .2164 
40      .2193 
50      .2221 

.2217    1.0243 
-.2247  .1.0249 
.2278    1.0256 

30 
40 
50 

.3007 
.3035 
.3062 

.3153 
.3185 
.3217 

1.0485 
1.0495 
1.0505 

13 

00      .2250 
10     .2278 
20      .2306 

.2309    1.0263 
.2339    1.0270 
.2370    1.0277 

18 

00 
10 
20 

.3090 
.3118 
.3145 

.3249 
.3281 
.3314 

1.0515 
1.0525 
1.0535 

30      .2834 
40      .2363 
50      .2391 

.2401    1.0284 
.2432    1.0291 
.2462    1.0299 

30 
40 
50 

.3173 
.3201 
.3228 

.3346 
.3378 
.3411 

1.0545 
1.0555 
1.0566 

14    00     .2419 
10      .2447 
20      .2476 

30      .2504 
40  i    .2532 
50  :    .2560 

i 

.2493    1.0306 
.2524    1.0314 
.2555    1.0321 

.2586    1.0329 
.2617    1.0337 
.2648    1.0345 

19 

00 
10 
20 

30 
40 
50 

.3256 
.3283 
.3311 

.3338 
.3365 
.8393 

.3443 
'.3476 
.3508 

.3541 
.3574 
.3607 

1.0576 
1.0587 
1.0598 

1.0608 
1.0619 
1.0631 

c 

14 

&                                                 '•* 

NATURAL  SINES,  TANGENTS  AND  SECANTS. 

(CONTINUED.) 

• 

Deg. 

Min. 

Sine. 

.3420 
.3448 
.3475 

Tangent.  Secant. 

I 

Deg. 

Min. 

00 
10 
20 

Sine.    Tangent. 

Secant. 

20 

00 
10 
20 

.3640 
.3673 
.3706 

1.0642 
1.0653 
1.0665 

25 

.4226      .4663 
.4253      .4699 
.4279      .4734 

1.1034 
1.1049 
1.1064 

30 
40 
50 

.3502 
.3529 
.3557 

.3739 
.3772 
.3805 

1.0676 
1.0688 
1.0700 

• 

30 
40 
50 

.4305 
.4331 
.4358 

.4770 
.4806 
.4841 

1.1079 
1.1095 
1.1110 

21 

00 
10 

20 

.3584 
.3611 
.3638 

.3839 
.3872 
.3906 

1.0711 
.1.0723 
1.0736 

26 

00 
10 
20 

.4384 
.4410 
.4436 

.4877 
.4913 
.4950 

1.1126 
1.1142 
1.1158 

30 
40 

50 

.3665 
.3692 
.3719 

.3939 
.3973 
.4006 

1.0748 
1.0760 
1.0773 

30 
40 
50 

.4462 
.4488 
.4514 

.4986 
.5022 
.5059 

1.1174 
1.1190 
1.1207 

22 

00 
10 
20 

.3746 
.3773 
.3800 

.4040 
.4074 
.4108 

1.0785 
1.0798 
1.0811 

27 

00 
10 
20 

.4540 
.4566 
.4592 

.5095 
.5132 
.5169 

1.1223 
1.1240 
1.1257 

30 
40 
50 

.3827 
.3854 
,3881 

.4142 
.4176 
.4210 

1.0824 
1.0837 
1.0850 

30 
40 
50 

.4617 
.4643 
.4669 

.5206 
.5243 
.5280 

1.1274 
1.1291 
1.1308 

23 

00 
10 
20 

.3907 
.3934 
.3961 

.4245 
.4279 
.4314 

1.0864 
1.0877 
1.0891 

28 

00 
10 
20 

.4695 
.4720 
.4746 

.5317 
.5354 
.5392 

1.1326 
1.1343 
1.1361 

30 
40 
50 

.3987 
.4014 
.4041 

.4348 
.4383 
.4417 

1.0904 
1.0918 
1.0932 

30 

40 
50 

.4772 
.4797 
.4823 

.5430 
.5467 
.5505 

1.1379 
1.1397 
1.1415 

24 

00 
10 
20 

.4067 
.4094 
.4120 

.4452 
.4487 
.4522 

1.0946 
1.0961 
1.0975 

29 

00 

10 
20 

.4848 
.4874 
.4899 

.5543 
.5581 
.5619 

1.1434 
1.1462 
1.1471 

30 
40 
50 

.4147 
.4173 
.4200 

.4557 
.4592 
.4628 

1.0989 
1.1004 
1.1019 

30 
40 
50 

.4924 
.4950 
.4975 

.5658 
.5696 
.5735 

1.1490 
1.1509 
1.1528 

c 

y— 

NATURAL  SINES 

,  TANGENTS  AND  SECANTS. 

(CONTINUED.) 

Deg.  Min. 

Sine. 

Tangent. 

Secant. 

Deg.  Min. 

Sine. 

.5736 
.5760 
.5783 

Tangent. 

Secant. 

30    00 
10 

20 

.5000 
.5025 
.5050 

.5774 
.5812 
.5851 

1.1547 
1.1566 
1.1586 

35 

00 
10 
20 

.7002 
.7046 
.7089 

1.2208 
1.2233 
1.2258 

30 
40 
50 

.5075 
.5100 
.5125 

.5890 
.5930 
.5969 

1.1606 
1.1626 
1.1646 

30     .5807 
40     .5831 
50     .5854 

.7133 
.7177 
.7221 

1.2283 
1.2309' 
1.2335 

31    00 

10 

!  20 

.5150 
.5175 
.5200 

.6009 
.6048 
.6088 

1.1666 
1.1687 
1.1707 

36 

00     .5878 
10     .5901 
20     .5925 

.7265 
.7310 
.7355 

1.2361 
1.2387 
1.2413 

30 
40 
J50 

.5225 
.5250 
.5275 

.6128 
.6168 
.6208 

1.1728 
1.1749 
1.1770 

30 
40 
60 

.5948 
.5972 
.5995 

.7400 
.7445 
.7490 

1.2440 
1.2467 
1.2494 

32    00 

10 

20 

.5299 
,5324 
.5348 

.6249 
.6289 
.6330 

1.1792 
1.1813 
1.1835 

37 

00  !  .6018 
10     .6041 
20     .6065 

.7536 
.7581 
.7627 

1.2521 
1.2549 
1.2577 

30 
40 
50 

.5373 
.5398 
.5422 

.6371 
-  .6412 
.6453" 

1.1857 
1.1879 
1.1901 

30 
40 
50 

.6088 
.6111 
.6134 

.7673 
.7720 
.7766 

1.2605 
1.2633 
1.2661 

33    00  '  .5446 

10     .5471 
20     .5495, 

.6494 
.6536 
.6577 

1.1924 
1.1946 
1.1969 

38 

00 
10 
20 

.6157 
.6180 
.6202 

.7813 
.7860 
.7907 

1.2690 
1.2719 
1.2748 

30     .5519 
40     .5544 
50     .5568 

.6619 
.6661 
.6703 

1.1992 
1.2015 
1.2039 

30 
40 
•50 

.6225      .7954 
.6248  ;  .8002 
.6271  i  .8050 

1.2778 
1.2808 
1.2837 

34    00     .5592 

10     .5616 
20     .5640 

.6745 
.6787 
.6830 

1.2062 
1.2086 
'  1.2110 

39 

00 
10 
20 

.6293  j  .8098 
.6316      .8146 
.6338      .8195 

1.2868 
1.2898 
1.2929 

30 
40 
50 

<  - 

.5664 
.5688 
.5712 

.6873 
.6916 
.6959 

1.2134 
1.2158 
1.2183 

30 
40 
50 

.6361 
.6383 
.6406 

.8243 
.8292 
.8342 

i  1.2960 
1.2991 
1.3022 

i 

NATURAL  SINES,  TANGENTS  AND  SECANTS. 

(CONTINUED.) 

Deg.  Min.    Sine. 

Tangent.  Secant. 

Deg.  Min. 

Sine.  Tangent. 

Secant. 

40    00     .6428 
10     .6450 
20     .6472 

.8391     1.3054 
.8441     1.3086 
.8491     1.3118 

45    00 

10 
20 

.7071  1.0000 
.7092  1.0058 
.7112  1.0117 

1.4142 
1.4183 
1.4225 

30     .6494 
40     .6517 
50     .6539 

41    00     .6561 
10     .6583 
20     .6604 

.8541     1.3151 
.8591     1.3184 
.8642     1.3217 

.8693     1.3250 
.8744  I  1.3284 
.8796     1.3318 

30 
40 
50 

46    00 

10 
20 

.7133  ;  1.0176 
.7153  i  1.0235 
.7173  1.0295 

.7193  l  1.0355 
.7214  1.0416 
.7234  1.0477 

1.4267 
1.4310 
1.4352 

1.4396 
1.4439 
1.4483 

30     .6626 
40     .6648 
50     .6670 

.8847     1.3352 
.8899     1.3386 
.8952     1.3421 

30 
40 
50 

.7254  1.0538 
.7274  1.0599 
.7294  1.0661 

1.4527 
1.4572 
1.4617 

42    00     .6691 
10     .6713. 
20     .6734 

.9004     1.3456 
.9057     1.3492 
.9110     1.3527 

47  ,  00 

:  10 

20 

.7314  1.0724 
.7333  1.0786 
.7353  1.0850 

1.4663 
1.4709 
1.4755 

30     .6756 
40     .6777 
50     .6799 

.9163     1.3563 
.9217     1.3600 
.9271     1.3636 

30 
40 
50 

.7373  1.0913 
.7392  1.0977 
.7412  1.1041 

1.4802 
1.4849 
1.4897 

43    00     .6820 
10     .6841 
20  I  .6862 

.9325     1.3673 
.9380     1.3711 
.9435     1.3748 

48    00 

10 

20 

.7431  1.1106 
.7451  1.1171 
.7470  :  1.1237 

1.4945 
1.4993 
1.5042 

30     .6884 
40  !  .6905 
50     .6926 

.9490     1.3786 
.9545     1.3824 
.9601    '1:3863 

30 
i  40 
50 

.7490  1.1303 
.7509  1.1369 
.7528  1.1436 

1.5092 
1.5141 
1.5192 

44    00     .6947 
10     .6967 
20     .6988 

.9657     1.3902 
.9713     1.3941 
.9770     1.3980 

49    00 

10 
20 

.7547  1.1504 
.7566  1.1571 
.7585  1.1640 

1.5243 
1.5294 
1.5345 

30  !  .7009 
40     .7030 
50     .7050 

'4  

.9827     1.4020 
.9884     1.4061 
.9942     1.4101 

30 
40 

50 

.7604  1.1708 
.7623  1.1778 
.7642  1.1847 

1.5398 
1.5450    1 
1.5504 

NATURAL  SINES 

,  TANGENTS  AND  SECANTS. 

Tangent. 

(CONTI 

Secant. 

VUED.) 

Deg.  Min. 

Deg.  :Min.    Sine. 

Sine. 

Tangent. 

Secant. 

50    00     .7660 
'  10     .7679 
:  20     .7698' 

1.1918 
1.1988 
1.2059 

1.5557 
1.5611 
1.5666 

55 

00 
10 
20 

.8192 
.8208 
.8225 

1.4281 
1.4370 
1.4460 

1.7434 
1.7507 
1.7581 

30  '  .7716 
40     .7735 
i.50     .7753 

1.2131 
1.2203 
1.2276 

1.5721 
1.5777 
1.5833 

30 
40 
50 

.8241 
.8258 
.8274 

1.4550 
1.4641 
1.4733 

1.7655 
1.7730 
1.7806 

51    00     .7771 
;  10     .7790 
20     .7808 

1.2349 
1.2423 
1.2497 

1.5890 
1.5948 
1.6005 

56 

00 
10 
20 

.8290 
.8307 
.8323 

1.4826 
1.4919 
1.5013 

1.7883 
1.7960 
1.8039 

30     .7826 
i  40     .7844 
;  50     .7862 

1.2572 
1.2647 
1.2723 

1.6064 
1.6123 
1.6183 

30 
40 
50 

.8339 
.8355 
.8371 

1.5108 
1.5204 
1.5301 

1.8118 
1.8198 
1.8279 

52    00     .7880 
i  10     .7898 
20     .7916 

1.2799 
1.2876 
1.2954 

1.6243 
1.6303 
1.6365 

57 

00 
10 
20 

.8387 
.8403 
.8418 

1.5399 
1.5497 
1.5597 

1.8361 
1.8443 
1.8527 

30     .7934 
,  40     .7951 
50     .7969 

1.3032 
.1.3111 
1.3190' 

1.6427 
1.6489 
1.6553 

30 
40 
50 

.8434 
.8450 
.8465 

1.5697 
1.5798 
1.5900 

1.8612 
1.8699 
1.8783 

53    00  '  .7986 
!  10  '  .8004 
20     .8021 

1.3270 
1.3351 
1.3432 

1.6616 
1.6681 
i  1.6746 

58 

00 
10 
20 

.8480 
.8496 
.8511 

1.6003 
1.6107 
1.6213 

1.8871 
1.8959 
1.9048 

'  30     .8039 
40     .8056 
50  :  .8073 

54  i  00     .8090 
10     .8107 
20     .8124 

1.3514 
1.3597 
1.3680 

1.3764 
'  1.3848 
1.3934 

1.6812 
i  1.6878 
1.6945 

I 

:  1.7013 

i  1.7081 
1  1.7151 

50 

30 
40 
50 

00 
10 
20 

.8526 
.8542 
.8557. 

.8572 
.8587 
.8601 

1.6319 
1.6426 
1.6534 

1.6643 
1.6753 
1.6864 

1.9139 
,  1.9230 
1.9323 
i 
1.9416 
1.9511 
1.9606 

30     .8141 
40     .8158 
50     .8175 

2u  

1.4019 
!  1.4106 
'  1.4193 

1.7221 
1.7291 
1.7362 

30 

40 
50 

.8616 
.8631 
.8646 

1.6977 
1.7090 
1.7205 

i 

1.9703 
1.9801 
1.9900 

'4 

NATURAL  SINES,  TANGENTS  AND  SECANTS. 

(CONTINUED.) 

Deg. 

Min. 

00 
10 
20 

Sine.    Tangent.  Secant. 

Deg.  Min. 

65     00 

10 

20 

Sine. 

Tangent. 

2.1445 
2.1609 

2.1775 

Secant. 

60 

.8660     1.7321    2.0000 
.8675     1.7437    2.0101 
.8689     1.7556    2.0204 

.9063 
.9075 
.9088 

2.3662 
2.3811 
2.3961 

30 
40 
50 

.8704     1.7675  ,  2.0308 
.8718     1.7796    2.0413 
.8732     1.7917    2.0519 

30     .9100 
40     .9112 
50     .9124 

2.1943 

2.2113 
2.2286 

2.4114 
2.4269 
2.4426 

61 

00 
10 
20 

.8746 
.8760 

.8774 

1.8040    2.0627 
1.8165    2.0736 
1.8291    2.0846 

66 

00 
10 
20 

.9135 
.9147 
.9159 

2.2460 
2.2637 
2.2817 

2.4586 
2.4748 
2.4912 

30 
40 
50 

.8788 
.8802 
.8816 

1.8418  !  2.0957 
1.8546    2.1070 
1.8676    2.1185 

30 
40 
50 

.9171 

.9182 
.9194 

2.2998 
2.3183 
2.3369 

2.5078 
2.5247 
2.5419 

62 

00 
10 
20 

.8829     1.8807 
.8843     1.8940 
.8857     1.9074 

2.1301 
2.1418 
2.1537 

67 

00 
10 
20 

.9205 
.9216 
.9228 

2.3559 
2.3750 
2.3945 

2.5593 
2.5770 
2.5949 

30 
40 
50 

.8870 
.8884 
.8897 

1.9210 
1.9347 
1.9486 

2.1657 
2.1786 
2.1902 

30 
40 
50 

.9239 
.9250 
.9261 

2.4141 
2.4342 
2.4545 

2.6131 
2.6316 
2.6504 

63 

00 
10 
20 

.8910 
.8923 
.8936 

1.9626 
1.9768 
1.9912 

2.2027 
2.2153 

2.2282 

68 

00 
10 
20 

.9272 
.9283 
.9293 

2.4751 
2.4960 
2.5172 

2.6695 
2.6888 
2.7085 

30 
40 
50 

.8949 
.8962 

.8975 

2.0057 
2.0204 
2.0353 

2.2412 
2.2543 

2.2677 

30 
40 
50 

.9304 
.9315 
.9325 

i  2.5386 
2.5605 
;  2.5826 

2.7285 
2.7488 
2.7695 

64 

00 
10 
20 

30 
40 
50 

.8988 
.9001 
.9013 

.9026 
.9038 
.9051 

2.0503 
2.0655 
2.0809 

2.0965 
2.1123 
2.1283 

2.2812 
2.2949 
2.3088 

2.3228 
2.3371 
2.3515 

69 

00 
10 

20 

30 
40 
50 

.9336 
.9346 
.9356 

.9367 
.9377 
.9387 

2.6051 
2.6279 
2.6511 

2.6746 
!  2.6985 
2.7228 

2.7904 
2.8117 
2.8334 

2.8555 
2.8779 
2.9006 

NATURAL 

SINES 

—  r 
,  TANGENTS  AND  SECANTS. 

Deg.  Min. 

Sine. 

Tangent. 

2.7475 
2.7725 
2.7980 

(CONTl 

Secant. 

NUED.) 

Deg.  Min 

.    Sine. 

• 
Tangent. 

Secant. 

70    00 

!  10 

20 

.9397 
.9407 
.9417 

2.9238 
2.9474 
2.9713 

75    00 

10 
20 

.9659 
.9667 
.9674 

3.7321 
3.7760 
3.8208 

3.8637 
3.9061 
3.9495 

30 
40 
50 

.9426 
.9436 
.9446 

2.8239 
2.8502 
2.8770 

2.9957 
3.0206 
3.0458 

30 
40 
50 

.9681 
.9689 
.9696 

3.8667 
3.9136 
3.9617 

3.9939 
4.0394 
4.0859 

71    00 

10  i 
20 

.9455 
.9465 
.9474 

2.9042 
2.9319 
2.9600 

3.0716 
3.0977 
3.1244 

76    00 

10 
20 

.9703 
.9710 
.9717 

4.0108 
4.0611 
4.1126 

4.1336 
4.1824 
4.2324 

30 
40 
50 

.9483 
.9492 
.9502 

2.9887  , 
3.0178 
3.0475  ! 

3.1515 
3.1792 
3.2074 

30 
40 
50 

.9724 
.9730 
i   .9737 

4.1653 
4.2193 
4.2747 

4.2837 
4.3362 
4.3901 

72    00 

10 

|20 

i 

30 
40 
50 

.9511 
.9520 
.9528 

.9537 
.9546 
.9555 

3.0777 
3.1084  i 
3.1397 

3.1716 
3;2041 
3.2371 

3.2361 
3.2653 
3.2951 

3.3255 
3.3565 
3.3881 

77    00 
10 

20 

30 
40 

50 

1   .9744 
.9750 
.9757 

.9763 
.9769 
.9775 

4.3315 
4.3897 
4.4494 

4.5107 
4.5736 
4.6382 

4.4454 
4.5022 
4.5604 

4.6202 
4.6817 
4.7448 

73    00 

10 
'20 

.9563 
.9572 
.9580 

3.2709 
3.3052 
3.3402 

3.4203 
3.4532 
3.4867 

78    00 

10 
20 

.9781 
.9787 
.9793 

4.7046 
4.7729 
4.8430 

4.8097 
4.8765 
4.9452 

30 
40 
50 

.9588 
.9596 
.9605 

3.3759 
3.4124 
3.4495 

3.5209 
3.5559 
3.5915 

30 
40 
50 

.9799 
.9805 
.9811 

4.9152 
4.9894 
5.0658 

5.0159 
5.0886 
5.1636 

74    00 
10 

20 

.9613 
.9621 
.9628 

3.4874 
3.5261 
3.5656 

3.6280 
3.6652 
3.7032 

79    00 
10 

20 

:    .9816 
.9822 
.9827 

5.1446 
5.2257 
5.3093 

5.2408 
5.3205 
5.4026 

30 
40 
,50 

.9636 
.9644 
.9652 

3.6059 
3.6470 
3.6891 

3.7420 
3.7817 
3.8222 

30 
40 
50 

.9833 
.9838 
.9843 

5.3955 
5.4845 
5.5764 

5.4874 
5.5749 
5.6653 

i5—                                                                                    —  1 
NATURAL  SINES,  TANGENTS  AND  SECANTS. 

(COiNTINUED.) 

Deg.  Min. 

Sine. 

Tangent.1  Secant. 

Deg.  <Min. 

Sine. 

Tangent. 

Secant. 

; 

80    00 

.9848 

5.6713   5.7588 

85    00 

.9962 

:  11.430 

11.474 

10 

.9853 

5.7694   5.8554 

10 

.9964 

11.826 

11.868 

20 

.9858 

5.8708   5.9554 

!  20 

.9967 

;  12.251 

12.291 

30 

.9863 

5.9758   6.0589 

30 

.9969 

12.706 

12.745 

40 

.9868 

6.0844    6.1661 

40 

.9971 

13.197 

13.235 

50 

.9872 

6.1970   6.2772 

50 

:9974 

13.727 

13.763 

81 

00 

.9877 

6.3138   6.3925 

86    00 

.9976 

14.301 

14.336 

10 

.9881 

6.4348    6.5121 

10 

.9978 

14.924 

14.958 

20 

.9886 

6.5606   6.6363 

20 

.9980 

15.605 

15.637 

j 

30 

.9890 

6.6912   6.7655 

30 

.9981 

16.350 

16.380 

40 

.9894- 

6.8269   6.8998 

40 

.9983 

17.169 

17.198 

50' 

.9899 

6.9682   7.0396 

50 

.9985 

18.075 

18.103 

82 

00 

.9903 

7.1154   7.1853 

87    00 

.9986 

19.081 

19.107 

10 

.9907 

7.2687   7.3372 

10 

.9988 

20.206 

20.230 

20 

.9911 

7.4287   7.4957 

20 

.9989 

21.470 

21.494 

30 

.9914 

7.5958   7.6613 

30 

.9990 

22.904 

22.926 

40 

.9918 

7.7704   7.8344 

40 

.9992 

24.542 

24.562 

50 

.9922 

7.9530   8.0156 

50 

.9993 

26.432 

26.451 

83 

00 

.9925  = 

8.1443   8.2055 

88    00 

.9994 

28.636 

28.654 

10 

.9929 

8.3450   8.4047 

10 

.9995 

31.242 

31.258 

!  20 

.9932 

8.5555   8.6138 

20 

.9996 

34.368 

34.382 

30 

.9936 

8.7769   8.8337 

30 

.9997 

38.188 

38.202 

40 

.9939 

9.0098   9.0652 

40 

.9997 

42.964 

42.976 

50 

.9942 

9.2553   9.3092 

50 

.9998 

49.104 

49.114 

84    00 

.9945 

9.5144   9.5668 

89    00 

.9998 

57.290 

57.299 

10 

.9948 

9.7882   9.8391 

10 

.9999 

68.750 

68.757 

20 

.9951 

10.0780  10.1275 

20 

.9999 

85.940 

85.946 

30 

.9954 

10.3854  10.4334 

30 

1.0000 

114.589 

114.593 

40 

.9957 

10.7119  10.7585 

40 

1.0000 

171.885 

171.888 

50 

.9959 

11.0594  11.1045 

50 

1.0000 

343.774 

343.775 

.! 

90    00 

1.0000 

Infinite. 

Infinite. 

1 

)2                                                  '*" 

LOGARITHMS  OP  NUMBERS. 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

10 

0000 

0043 

0086 

0128 

0170 

0212 

0253  !  0294 

0334 

0374 

40 

11 

0414 

0453 

0492 

0531 

0569 

060710645 

0682 

0719 

07551  37 

12 

0792 

0828 

0864 

0899 

0934 

0969 

1004 

1038 

1072 

1106;  33 

13 

1139 

1173 

1206 

1239 

1271 

1303 

1335 

1367 

1399 

14301  31 

14 

1461 

1492 

1523 

1553 

1584 

1614 

1644 

1673 

1703 

1732  29 

15 

1761 

1790 

1818 

1847 

1875 

1903 

1931 

1959 

1987 

2014  i  27 

16 

2041 

2068 

2095 

2122 

2148 

2175 

2201 

2227 

2253 

22791  25 

17 

2304 

2330 

2355  !  2380 

2405 

2430 

2455 

2480 

2504 

2529!  24 

18 

2553 

2577 

2601 

2625 

2648 

2672 

2695 

2718 

2742 

2765!  23 

19 

2788 

2810 

2833 

2856 

2878 

2900 

2923 

2945 

2967 

2989  21 

I 

20 

3010 

3032 

3054  3075  3096 

3118 

3139 

3160  3181 

3201  21 

21 

3222 

3243 

3263 

3284  3304 

3324 

3345  3365 

3385 

3404 

20 

22 

3424 
3617 

3444 
3636 

3464 
3655 

348313502 
3674  3692 

3522 

3711 

3541 
3729 

3560 

3747 

3579 
3766 

3598 
3784 

19 
18 

24 

3802 

3820 

3838  3856 

3874 

3892 

3909 

3927 

3945 

3962 

17 

25  3979 

3997 

4014 

4031 

4048 

4065 

4082 

4099 

4116! 

4133 

17 

26  4150 

4166 

4183  4200 

4216 

423214249 

4265 

4281 

4298 

16 

J 

27  14314 

4330 

4346  4362 

4378 

4393 

4409 

4425 

4440 

4456 

16 

28  4472 

4487 

4502  451  § 

4533 

4548 

4564 

4579 

4594 

4609 

15 

29 

4624 

4639 

4654 

4669 

4683 

4698 

4713 

4728 

4742 

4757  14 

i 

30 

4771 

4786 

4800 

4814 

4829 

4843.4857 

4871 

4886; 

4900  1  14 

31 

4914 

4928 

4942 

4955 

4969 

4983  4997 

5011 

5024 

5038  13 

32 
33 

5051 
5185 

5065 
5198 

5079 
5211 

5092 
5224 

5105 
5237- 

5119)5132 
525015263 

5145  j  5159 
527615289 

5172 
5302 

13 
13 

34 

5315 

5328 

5340 

5353 

5366 

5378  5391 

5403 

5416 

5428  13 

35 

5441 

5453 

5465  15478 

5490 

5502  j  5514 

552715539 

5551 

12 

36 

5563 

5575 

5587  5599 

5611 

5623  5635 

5647  15658 

5670 

12 

37 

5682 

5694 

5705  5717 

5729 

5740 

5752 

5763 

5775 

5786 

12 

38 

5798 

5809 

5821  5832 

5843 

5855 

5866 

587715888 

5899 

IB- 

39 

5911 

5922 

5933  !  5944 

5955 

5966 

5977 

5988 

5999 

6010 

11 

j 

. 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

y                    153 

LOGARITHMS  OF  NUMBERS—  Continued. 

No. 

0 

1   2 

3 

4 

5 

6 

7 

8 

9  Diff. 

40 

41 
42 
43 

6021 

6031  6042 

6053 

6064 

6075 

6085 

6096 

6201 
6304 
6405 

6107 

6212 
6314 
6415 

6117 

6222 
6325 
6425 

11 

10 
10 
10 

6128 
6232 
6335 

6138  6149 
6243  6253 
6345  6355 

6160 
6263 
6365 

6170 
6274 
6375 

6180 
6284 
6385 

6191 
6294 
6395 

44 
45 
46 

6435 
6532 
6628 

6444  6454 
6542  6551 
6637  6646 

6464 
6561 
6656 

6474 
6571 
6665 

6484 
6580 
6675 

6493 
6590 
6684 

6503 
6599 
6693 

6513 
6609 
6702 

6522 
6618 
6712 

10 
10 
9 

47 
48 
49 

50 

51 
52 
53 

6721 
6812 
6902 

6730  6739 
6821  6830 
6911  6920 

6749 
6839 
6928 

6758 
6848 
6937 

7024 

6767 
6857 
6946 

6776 
6866 
6955 

6785 
6875 
6964 

6794 
6884 
6972 

6803 
6893 
6981 

9 
9 
9 

9 

8 
8 
8 

6990 

7076 
7160 
7243 

6998  7007 

7084  7093 
7168  7177 
7251  7259 

7016 

7101 
7185 
7267 

7033 

7042 

7050 

7059 

7067 

7152 
7235 
7316 

7110 
7193 

7275 

7118 
7202 

7284 

7126 
7210 
7292 

7135 
7218 
7300 

7143 
7226 
7308 

54 
55 
56 

7324 
7404 
7482 

7332  7340 
741217419 
7490  7497 

7348 
7427 
7505 

7356 
7435 
7513 

7364 
7443 
7520 

7372 
7451 
7528 

7380 
7459 
7536 

7388 
7466 
7543 

7396 

7474 
7551 

8 
8 
8 

57 
58 
59 

60 

61 
62 
63 

7559 
7634 
7709 

7566  '7574 
76427649 
7716  7723 

7582 
7657 
7731 

7589 
7664 
7738 

7810" 

7597 
7672 
7745 

7604 
7679 
7752 

7612 
7686 
7760 

7619 
7694 
7767 

7627 
7701 
7774 

7' 
8 
8 

7 

7 
6 

7 

7782 

7789  7793 

7803 

7818 

7889 
7959 

8028 

7825 

7832 

7903 
7973 
8041 

7839 

7846 

7853 
7924 
7993 

7860  7868 
7931  7938 
8000  8007 

7875 
7945 
8014 

7882 
7952 
8021 

7898 
7966 
8035 

7910  7917 
7980  7987 
804818055 

64 
65 
66 

8062 
8129 
8195 

8069  8075 
8136  8142 
8202  8209 

8082 
8149 
8215 

8089 
8156 
8222 

8096 
8162 
8228 

8102 
8169 
8235 

8109 
8176 
8241 

8116 
8182 
8248 

8122 
8189 
8254 

7 
6 
7 

67 
68 
69 

8261 
8325 
8388 

8267  8274 
8331  8338 
8395  8401 

8280 
8344 

8407 

8287 
8351 
8414 

8293 
8357 
8420 

5 

8299 
8363 

8426 

8306  8312 
8370!  8376 
8432:8439 

8319 
8382 
8445 

6 
6 
6 

No. 

0 

I   2 

3 

4 

6 

7 

8 

9 

Diff. 

^                     154 

23—                                             —  |i 
LOGARITHMS  OF  NUMBERS—  Continued. 

No. 

0   1 

2 

3 

4 

8476 

8537 
8597 
8657 

5 

8482 

8543 
8603 
8663 

6 

7 

8 

9 

Diff. 

7 

6 
6 
6 

70 

71 
72 
73 

8451  8457 

8463 

8470 

8531 
8591 
8651 

8488 

8494  8500 

8506 

8513  :  8519 
8573  8579 
8633  8639 

8525 
8585 
8645 

8549  1  8555 
8609  !  8615 
8669  j  8675 

8561 
8621 
8681 

8567 
8627 
8686 

74 
75 
76 

8692  8698 
.8751  8756 
8808  8814 

8704 
8762 
8820 

8710 
8768 
8825 

8716 

8774 
8831 

8722 
8779 
8837 

8727 
8785 
8842 

8733 
8791 
8848 

8739 
8797 
8854 

8745 
8802 
8859 

6 
6 
6 

.  77 
78 
79 

80 

81 
82 
83 

8865  8871 
8921  8927 
8976  8982 

9031  9036 

8876 
8932 
8987 

8882 
8938 
8993 

8887 
8943 
8998 

8893 
8949 
9004 

9058 

9112 
9165 
9217 

8899 
8954 
9009 

8904 
8960 
9015 

8910 
8965 
9020 

9074 

8915 
8971 
9025 

6 
5 
6 

6 

5 
5 
5 

9042  9047  9053 

9063 

9117 
9170 
9222 

9069 

9079 

9085  9090 
9138  9143 
9191  9196 

9096 
9149 
9201 

9101 
9154 
9206 

9106 
9159 
9212 

9122 
9175 

9227 

9128 
9180 
9232 

9133 
19186 
9238 

84 
85 
86 

9243  ]  9248 
9294  9299 
9345  9350 

9253 
9304 
9355 

9258 
9309 
9360 

9263 
9315 
9365 

9269 
9320 
9370 

9274 
9325 
9375 

9279 
9330 
9380 

9284 
9335 
9385 

9289 
9340 
9390 

5 
5 
5 

87 
88 
89 

90 

91 
92 
93 

9395  9400 
9445  9450 
9494  9499 

9405 
9455 
9504 

9410 
9460 
9509 

9415 
9465 
9513 

9420 
9469 
9518 

9425 
9474 
9523 

9430 
9479 
9528 

9435 
9484 
9533 

958l" 

9440 
9489 
9538 

5 
5 
4 

4 

5 
5 
4 

9542  9547 

9552 

9557 

9562 

9566 

9614 
9661 
9708 

9571 

9576 

9586 

9590  9595 
9638  9643 
9685  9689 

9600 
9647 
9694 

9605 
9652 
9699 

9609 
9657 
9703 

9619 
9666 
9713 

9624 
9671 
9717 

9628 
9675 
9722 

9633 
9680 
9727 

94 
95 
96 

9731  9736 
9777  9782 
9823  !  9827 

9741 
9786 
9832 

9745 
9791 
9836 

9750 
9795 
9841 

9754 
9800 
9845 

9759 
9805 
9850 

9763 
9809 
9854 

9768 
9814 
9859 

9773 
9818 
9863 

4 
5 
5 

97 
98 
99 

9868  9872 
9912'9917 
9956  9961 

9877 
9921 
9965 

2 

9881 
9926 
9969 

9886 
9930 
9974 

9890 
9934 
9978 

9894 
9939 
9983 

9899 
9943 
9987 

9903 
9948 
9991 

9908 
9952 
9996 

4 
4 
4 

No. 

0  |  1 

3 

4 

5 

6 

7 

8 

9 

Diff. 

**                    155                    '*• 

WEIGHT    OF 
A    CUBIC    FOOT     OF    SUBSTANCES. 

Average 

NAMES  OF  SUBSTANCES.  Weight 

LBs. 

Anthracite,  solid,  of  Pennsylvania,  93 

"           broken,  loose,  54 

"                "        moderately  shaken,  58 

"           heaped  bushel,  loose,  (8O) 

Ash,  American  white,  dry,  38 

Asphaltum,  87 

Brass,  (Copper  and  Zinc,)  cast,        -         -  504 

«      rolled,  524 

Brick,  best  pressed,  150 

"      common  hard,  125 

"      soft,  inferior,  100 

Brickwork,  pressed  brick,  140 

"           ordinary,  112 

Cement,  hydraulic,  ground,  loose,  American,  Rosendale,          56 

"               "                 "           "             "           Louisville,  50 

"               "                 "           "      English,  Portland,  -             90 

Cherry,  dry,                                                                    .  -  42 

Chestnut,  dry,    -  41 

Coal,  bituminous,  solid,  84 

"             "            broken,  loose,  49 

"             "            heaped  bushel,  loose,            -         -  -      (74) 

Coke,  loose,  of  good  coal,  27 

"         "       heaped  bushel,    -  (38) 

Copper,  cast,  542 

rolled,  548 

Earth,  common  loam,  dry,  loose,          -         -         -  76 

"           "             "       "    moderately  rammed,         -  -       95 

"        as  a  soft  flowing  mud.     -  108 

Ebony,  dry,  76 

Elm,  dry,  35 

Flint,  -      162 

Glass,  common  window,     -         -         -  157 

156 


WEIGHT  OF  SUBSTANCES— Continued. 

Average 

NAMES  OF  SUBSTANCES.  Weight. 

Lbs. 

Gneiss,  common.            _______  1Q& 

Gold,  cast,  pure,  or  24  carat,       _____       1204 

"      pure,  hammered,  ______  1217 

Granite,                                                            _  170 
Gravel,  about  the  same  as  sand,  which  see. 

Hemlock,  dry,      ---_.._.  25 

Hickory,  dry,    -__-__.  53 

Hornblende,  black,        -                            -  203 

Kce,           -        -       '-•      -        -        -        -        -        -  58.7 

Iron,  cast,     -----_-__  450 

i<     wrought,  purest,         -                  -         -         -         -  485 

average,                                                         -  480 

Ivory, 114 

Lead,                                                                                          -  711 

Lignum  Vitae,  dry,    _______  83 

Lime,  quick,  ground,  loose,  or  in  small  lumps,          -         -  53 

"            "      thoroughly  shaken,   -  75 

"          "           "            "      per  struck  bushel,           -         *.  (66) 

Limestones  and  Marbles,  -         -         -         -         _         -  168 

"                       "         loose,  in  irregular  fragments,       -  96 

Mahogany,  Spanish,  dry,  '          -                  -         -         -  53 

"           Honduras,  dry,    -         -         -         -         -  35 

Maple,  dry,      -        -         -        -         -         -        -         _  49 

Marbles,  see  Limestones. 

Masonry,  of  granite  or  limestone,  well  dressed,            -  165 

"    mortar  rubble, 154 

"          "   dry            "       (well  scabbled,)         -         -  138 

"          "    sandstone,  well  dressed,       -  144 

Mercury,  at  32°  Fahrenheit,        -         -        ...  849 

Mica,            -         -        _ 183 

Mortar,  hardened,     -                   -         -         -         -         -  103 

Mud,  dry,  close,  -         -         -         -         -         -  80  to  110 

"      wet,  fluid,  maximum,         -                   -         -         -  120 

Oak,  live,  dry,       --         -         _-_         _         _         .  59 


WEIGHT  OF  SUBSTANCES— Continued. 

Average 

NAMES  OF  SUBSTANCES.  Weight. 

Lfe. 
Oak,  white,  dry,         -------  52 

"     other  kinds,  -         -         -         -         -         -    32  to  45 

Petroleum,        ____--_-  55 

Pine,  white,  dry,  _______       25 

"     yellow,  Northern,      _.-___  34 

"          "        Southern,          -____-       45 

Platinum,  1342 

Quartz,  common,  pure,  -         -         -         -         -         -165 

Rosin, 69 

Salt,  coarse,  Syracuse,  N.  Y.  -•.-.-.       45 

"     Liverpool,  fine,  for  table  use,      -  49 

Sand,  of  pure  quartz,  dry,  loose,     -  90  to  106 

"     well  shaken,  99  to»  117 

"     perfectly  wet,       -  120  to  140 

Sandstones,  fit  for  building,        _____          151 
Shales,  red  or  black,      -        ...  -  162 

Silver,      -  -         655 

Slate,   .         -  175 

Snow,  freshly  fallen,  5  to  12 

"       moistened  and  compacted  by  rain,         -         -     15  to  50 
Spruce,  dry,      __---_--  25 

Steel, 490 

Sulphur,  125 

Sycamore,  dry,      --------37 

Tar,  62 

Tin,  cast,      ---------    459 

Turf  or  Peat,  dry,  unpressed,      -        -        -         -         20  to  30 

Walnut,  black,  dry,        ___-_-_       38 
Water,  pure  rain  or  distilled,  at  60°  Fahrenheit,  -       62 1/3 

"       sea, 64 

Wax,  bees,        .-- 60.5 

Zinc  or  Spelter,     --_-__--    437 

Green  timbers  usually  weigh  from  one-fifth  to  one-half  more 
than  dry. 

-*-        158 8 


WINDOW    GLASS. 

Window  Glass  is  sold  by  the  box,  which  contains,  as  nearly  as 

may  be,  50  square  feet,  whatever  may  be  the  size  of  panes. 
The  thickness  of  ordinary  or  "single  thick"  Window  Glass  is 

about  1-16  of  an  inch,  and  of  "double  thick  "  nearly  1-8  of  an  inch. 

'I 

"he  tensile  strength  of  common  glass  varies  from  2000  Ibs.  to 

3000  Ibs.  per  square  inch,  and  its  crushing  strength  from  6000  Ibs. 
to  10000  Ibs. 

The  following  is  the  list  of  the  Pittsburgh  City  Glass  Works, 
Cunninghams  &  Co.,  Proprietors.     Other  sizes  may  be  made  to 

order. 

Sizes. 
In. 

Lights 
per  Box 

No. 

Sizes. 
In. 

Lights 
perBoi. 
No. 

Lights 
SlTzes-     perBoi. 
Itt-         No. 

Sizes. 
In. 

Lights 
perBoi 

No. 

Lights 
No. 

6X    8 

150 

11  X  24       27 

14  X  18       29 

18  X  18 

22 

24  X  30 

10 

7X    9 

115 

26       25 

20       26 

20 

20 

32 

10 

8X  10 

90 

28 

23 

22 

24 

22 

18 

34        9 

12 

'      75 

30 

22 

24 

22 

24 

17 

36        9 

13 

69 

32 

20 

26 

20 

26 

16 

38        8 

*  14 

64 

34 

19 

28 

19 

28 

14 

40        8 

15 

60 

36 

18 

30 

17 

30 

14 

42        7 

16 

56 

38 

17 

32 

16 

32 

13 

44 

7 

18 

50 

46       16 

34 

15 

34 

12 

46 

7 

20 

45 

42       15 

36 

14 

36 

11 

48 

6 

9X  U 

73 

12  X  12      50 

38 

14 

38 

11 

26  X  26 

11 

12 

67 

13 

46 

40 

13 

40 

10 

28 

10 

13 

62 

14 

43 

42 

12 

42 

10 

30 

9 

14 

57 

15 

40 

44 

12 

44 

9 

32 

9 

15 

53 

16!     38 

46 

11 

46 

9 

34 

8 

16 

50 

18  |     34 

15  X  15 

32 

20X  20 

18 

36 

8 

18 

44 

19 

32 

16 

30 

22 

17 

38 

7' 

20 

40 

20 

30 

18 

27 

24 

15 

40 

7 

22 

36 

22 

27 

20 

24 

26 

14 

42 

7 

10  X  12 

60 

24 

25 

22 

22 

28 

13 

44 

6 

13 

55 

26 

23 

24 

20 

30 

12 

46 

6 

14 

52 

28 

22 

26 

19 

32 

11 

48 

6 

15  i      48 

30 

20 

28 

17 

34 

11 

28X28 

9 

16 

45 

32 

19  - 

30 

16 

36 

10 

30 

9 

18 

40 

34 

18 

32 

15 

38 

10 

32 

8 

19 

38 

36 

17 

34 

14 

40 

9 

34 

8 

20 

36 

38 

16 

36 

13 

42 

9 

36 

7 

22 

33 

40 

15 

38 

13 

44 

8 

38 

7 

24 

30 

42 

14 

40 

12 

46 

8 

40 

7 

26 

28 

13  X  15 

37 

42 

11 

22  X  22 

15 

42 

6 

28 

25 

16 

35 

44 

11 

24 

14 

44 

6 

30 

24 

18 

31 

16  X  16 

28 

26 

13 

46 

6 

32 

22 

20 

28 

18 

25 

28 

12 

48 

5 

34 

21 

22 

25 

20 

23 

30 

11 

30X30 

8 

36 

20 

24 

23 

22      21 

32 

10 

32'      7 

38 

19 

26 

21 

24       19 

34 

10 

34        7 

40 

18 

28 

20 

26 

17 

36 

9 

36 

7 

42 

17 

30 

18 

28 

16 

38        9 

38 

7 

11  X  12 

55 

32 

17 

30 

15 

40 

8 

40 

6 

14 

47 

34 

16 

32 

14 

42 

8 

42 

6 

15 

44 

36 

15 

34 

13 

44 

7 

44 

6 

16 

41 

•     38       15 

36 

13 

46 

7 

46 

5 

18 

37 

40       14 

38 

12 

48 

7 

48 

5 

19 

34 

42      13 

40 

11 

24X  24 

12 

50 

5 

20 

33 

14  X  14       37 

42 

11 

26       12 

22 

30 

16       32 

44 

10 

28       11 

c 

LINEAR    EXPANSION    OP    SUBSTANCES 

BY 

HEAT. 

To  find  the  increase  in  the 

length  of  a  bar  of  any  material  clue 

to  an  increase  of  temperature,  multiply  the  number  of  degrees 

of  increase  of  temperature  by  the  coefficient  for  100  degrees  and 

by  the  length  of  the  bar,  and 

divide  by  100. 

NAME  OF  SUBSTANCE. 

Coefficient  for  100  °   Coefficient  for  180° 
Fahrenheit.         Fahrenheit,  or  100° 

Centigrade. 

Baywood,  (in  the  direction  of  the  J 

.00026 

TO 

.00046 

TO 

grain,  dry,) 

I 

.00031 

.00057 

Brass,  (cast,)    - 

- 

.00104 

.00188 

"       (wire,) 

.O0107 

.00193 

Brick,  (fire,)     - 

- 

.0003 

.0005 

Cement,  (Roman,)  - 

- 

.0008 

.0014 

Copper, 

.0009 

.0017 

Deal,  (in  the  direction  of  the  grain,  J 
dry,)      -            -                         -{ 

.00024 

.00044 

Glass,  (English  flint,)  - 

- 

.00045 

.00081 

"      (French  white  lead,) 

- 

.00048 

.00087 

Gold.. 

- 

.0008 

.0015 

Granite,  (average,) 

- 

.00047 

.00085 

Iron,  (cast,)    - 

- 

.0006 

.0011 

"      (soft  forged,) 

•- 

.0007 

.O012 

"     (wire,)  - 

- 

.0008 

.0014. 

Lead, 

- 

.0016 

.0029 

.00036 

.00065 

Marble,  (Carrara,)  - 

TO 

TO 

.0006 

.0011 

Mercury, 

.0033             .0060 

Platinum, 

- 

.0005             .0009 

{• 

.0005             .0009 

Sandstone,  - 

TO                             TO 

f 

.0007             .0012 

Silver, 

.0011             .002 

Slate,  (Wales,) 

.0006             .001 

Water,    (varies  considerably 

wlthf        .0086             .0155 

the  temperature,) 

i  . 

MENSURATION. 


LENGTH. 

Circumference  of  circle  =  diameter  X  3.1416. 

Diameter  of  circle  =  circumference  X  0.3183. 

Side  of  square  of  equal  periphery  as  circle  =  diameter  X  0.7854. 

Diameter  of  circle  of  equal  periphery  as  square  =  bide  X  1.2732; 

Side  of  an  inscribed  square  =  diameter  of  circle  X  0.7071. 

Length  of  arc  =  No.  of  degrees  X  diameter  X  0.008727. 

Circumference  of  circle  whose  diameter  is  1  = 


TT  =  3.14159265. 


log.7r=0.4971499. 
-,/  7r=1.772454. 

TT  2=9.869604. 
c2 


0.318310. 


=  0.101321. 


0.564190. 


2v 


or,  very  nearly,  =  - — 


AREA. 

Triangle  =  base  X  half  perpendicular  hight. 
Parallelogram  =  base  X  perpendicular  hight. 
Trapezoid  =  half  the    sum    of  the  parallel  sides  X   perpen- 
dicular hight. 

Trapezium,  found  by  dividing  into  two  triangles. 
Circle  =  diameter  squared  X  0.7854  ;  or, 

=  circumference  squared  X  0.07958. 
Sector  of  circle  =  length  of  arc  X  half  radius. 


161 


MENSURATION— Continued. 

Segment    of   circle  =   area    of   sector   less    triangle ;     also,    for 

4  v  i/                        c~2~ 
Hat  segments  very  nearly  =  —    -r  0.388  v-   -\ j— 

Side  of  square  of  equal   area  as  circle  =  diameter  X    0.8862 ; 

also,  =  circumference  X  0.2821. 

Diameter  of  circle  of  equal  area  as  square  =  side  X  1.1284. 
Parabola  =  base  X   /i  hight. 

Ellipse  =  long  diameter  X  short  diameter  X  0.7854. 
Regular  polygon  =  sum  of  sides  X  half  perpendicular  distance 

from  center  to  sides. 
Surface  of  cylinder  =  circumference   X  hight  X    area  of  both 

ends. 
Surface  of  sphere  =  diameter  squared  x  3.1416; 

also,  =  circumference  X  diameter.       % 
Surface  of  a  right  pyramid  or  cone  =  periphery  or  circumference 

of  base  X  half  slant  hight. 
Surface  of  a  frustrum  of  a  regular  right  pyramid  or  cone  =  sum 

of  peripheries   or   circumferences  of  the  two  ends   X   half 

slant  hight  -j-  area  of  both  ends. 

The  following  formulae  are  used  to  obtain  the  areas  of 
irregular  plane  surfaces  which  are  bounded  by  a  base  line,  "cc" 
and  two  ordinates,  "«"  and  "£,"  as  per  figure. 


The  formulae  are  given  in  the  order  of  their  accuracy,  be- 
ginning with  the  most  accurate. 

The  sift-face  is  divided  into  any  number  (n}  of  parallel  strips 
having  the  same  widths,  d,  and  whose  middle  ordinates  are 
represented  by  h  h  h h  and  //. 

123  n — 1          n 

162 


•88 


MENSURATION—  Continued. 


I.     Area  =  d  X  S  h  +(8  a  +  ly-9  h  )  +8b  +  t^j 

(Francke's  rule.) 

II.  Area  =  d   X  S  h  +   ^  --(a  -  h)  +  -A-  (b  -  hj 

(Poncelet's  rule.) 

III.  Area  =  d  X  §  h. 

These  formulae  are  more  convenient  for  use  than  Simpson's 
rule,  and  I  and  II  give  generally  and  III  sometimes  more 
accurate  results. 

^  stands  for  sum  of. 


SOLID    CONTENTS. 

Prism,  right  or  oblique,  =  area  of  base  X  perpendicular  hight. 
Cylinder,  right  or  oblique,  =  area  of  section  at  right  angles  to 

sides  X  length  of  side. 
Sphere  =  diameter  cubed  X  0.5236. 

also,  =  surface  X  l/6  diameter. 
Pyramid  or  cone,  right  or  oblique,  regular  or  irregular,  =  area 

of  base  X  /•£  perpendicular  hight. 


PRISMOIDAL  FORMULA. 

A  prismoid  is  a  solid  bounded  by  six  plane  surfaces,  only 
two  of  which  are  parallel. 

To  find  the  contents  of  a  prismoid,  add  together  the  areas  of  the 

.  two   parallel  surfaces  and  four  times  the  area  of  a  section 

taken  midway  between  and  parallel  to  them,  and  multiply 

the  sum  by  i/£th  of  the  perpendicular  distance  between  the 

parallel  surfaces. 


WEIGHTS  AND  MEASURES. 

AVOIRDUPOIS  OR  ORDINARY  COMMERCIAL  WEIGHT. 

UNITED   STATES   AND 

BRITISH. 

Ton. 

Owts. 

Poandi. 

Ounces. 

1. 
0.050 

20. 
1. 
0.0089 

2240. 
112. 
1. 
0.0625 

35840. 
1792. 
16. 
1. 

1  pound  =  27.7  cubic  inches 
density,  (39°  Fahrenheit.) 

of  distilled  water  at 

its  maximum 

LONG 

MEASURE. 

UNITED   STATES   AND 

BRITISH. 

Miles. 

Rods.              Yards. 

Feet. 

Inches. 

1. 

0.003125 
0.000568 
0.0001894 
0.0000158 

320.                1760. 
1.                     5.5 
0.1818               1. 
0.0606               0.3333 
0.005051            0.02778 

5280. 
16.5 
'3. 
1. 
0.08333 

63360. 
198. 
36. 
12. 

1. 

The  British  measures  are  shorter  than  those  of  the  U.  S.  by 
about  1  part  in  17230  or  3.677  inches  in  a  mile. 
A  fathom  =  6  feet.     A  Gunter's  surveying  chain  =  66  feet 
or  4  rods,  80  chains  making  a  mile. 

SQUARE    OR    LAND 

MEASURE 

UNITED   STATES   AND    BRITISH. 

Sq.  Miles.     1 

Lores.       Sq.  Rods. 

Sq.  Yards.        Sq.  Feet. 

Sq.  Inches. 

1.           C 

40.       102400.        3097600.      27878400. 
1.            160.            4840.           43560.          6272640. 
1.               30.25           272.25         39204. 
0.0331           1.                 9.0            1296. 
0.111              1.                144. 
0.00694           1. 

"                                                   164                                                  r* 

WEIGHTS  AND  MEASURES— Continued. 

CUBIC    OR    SOLID    MEASURE. 

UNITED   STATES  AND   BRITISH. 

1728  cubic  inches  =  1  cubic  foot. 

27  cubic  feet  =  1  cubic  yard. 

A  cord  of  wood  =  4'  X  V  X  8'  =  128  cubic  feet. 
A  perch  of  masonry  =  16.5'  X  1.5'  X  1'  =  24.75  cubic  feet, 
but  is  generally  assumed  at  25  cubic  feet. 

DRY    MEASURE.. 

UNITED   STATES    ONLY. 


Struck  Bush  I     Pecks. 

Quarts. 

Pints. 

Gallons. 

Cubic  Inch. 

1 

\ 

32. 
8. 
1. 
0.5 
4. 

64 
16 

2 
1 

8 

8. 
2. 
0.25 
0.125 
1. 

2150. 
537.6 
67.2 
33.6 
268.8 

A  gallon  of  liquid  measure  =  231  cubic  inches. 

A  heaped  bushel  =  1 14'  struck  bushels.  The  cone  in  a  heaped 
bushel  must  be  not  less  than  6  inches  high. 

A  barrel  of  U.  S.  hydraulic  cement  =  300  to  310  Ibs.,  usually, 
and  of  genuine  Portland  cement  =  425  Ibs. 

To  reduce  U.  S.  dry  measures  to  British  imperial  of  the  same 
name,  divide  by  1.032. 

NAUTICAL   MEASURE. 

A  nautical  or  sea  mile  is  the  length  of  a  minute  of  longitude 
of  the  earth  at  the  equator  at  the  level  of  the  sea.  It  is  assumed 
=  6086.07  feet  ==  1.152664  statute  or  land  miles  by  the  United 
States  Coast  Survey. 

3  nautical  miles  =  1  league. 


165 


COMPARATIVE    TABLE    OF 
UNITED  STATES  AND  FRENCH  MEASURES. 


MEASURES.  No. 

One  grain  =  gramme,  O.0648 

One  pound  avoirdupois  =  kilogramme,      -  -         O.4536 

One  ton  of  2240  Ibs.  =  tonnes,             -             -  1.0160 

One  ton  of  2000  Ibs.  =  tonne,        -  0.9071 

One  inch  =  millimetres,                                       -  25.40O 

One  foot  =  metre,  -         O.3048 

One  mile  =  kilometres,  1.6094 

One  square  inch  =  square  millimetres,      -  -            645.2 

One  square  foot  =  square  metre,  0.09291, 

One  acre  =  are  (100  square  metres),         -  40.47 

One  square  mile  =  square  kilometres,  2.590 

One  cubic  inch  =  cubic  centimetres,         -  16.39 

One  cubic  foot  =  cubic  metre,  O.02832 

One  cubic  yard  =  cubic  metre,     -  -         0.7646 

One  quart  dry  measure  =  litres,  1.1O1 

One  quart  liquid  or  wine  measure  =  litre,  -         O.9465 

One  foot  pound  =  kilogrammetre,       -  0.1383 

One  pound  per  foot  =  kilogrammes  per  metre,  -            1.488 

One  thousand  pounds  per  square  inch  =  kilogramme 

per  square  millimetre,  0.703 

One  pound  per  square  foot  =  kilogrammes  per 

square  metre,  4.882 

One   pound    per   cubic   foot   =   kilogrammes  per 

cubic  metre,  16.02 

One  degree  Fahrenheit  =  degree  centigrade,  O.5556 
166 


3  —                                                                                —  ? 

COMPARATIVE    TABLE    OF 
FRENCH  AND  UNITED  STATES  MEASURES. 

MEASURES. 

No. 

One  gramme  =  grains, 

15.433 

One  kilogramme  =  pounds  avoirdupois,    - 

2.2047 

Oncxtonne  =  tons  of  2240  Ibs. 

0.9843 

One  tonne  =  tons  of  2000  Ibs. 

1.1024 

One  millimetre  =  inch, 

0.0394 

One  metre  =  feet, 

3.2807 

One  kilometre  =  mile, 

0.6213 

One  square  millimetre  =  square  inch, 

0.00155 

One  square  metre  =  square  feet, 

10.763 

One  are  (100  square  metres)  =  acres, 

0.02471 

One  square  kilometre  =  square  mile, 

0.3861 

One  cubic  centimetre  —  cubic  inch, 

0.0610 

One  cubic  metre  or  stere  =  cubic  feet, 

35.3105 

One  cubic  metre  =  cubic  yards,     - 

1.3078 

One  litre  (one  cubic  decimetre)  =  cubic  inches, 

61.017 

One  litre  =  quarts,  dry.  measure,  - 

0.908 

One  litre  =  quarts,  liquid  or  wine  measure,     - 

1.0566 

One  kilogrammetre  =  foot  pounds, 

7.2331 

One  kilogramme  per  metre  =  pounds  per  foot, 

0.6720 

One  kilogramme  per  square  millimetre  =  pounds 

per  square  inch,    - 

1422 

One  kilogramme   per  square  metre  =  pounds  per 

square  foot, 

0.2048 

One  kilogramme   per   cubic  metre  =  pounds  per 

cubic  foot, 

0.0624 

One  degree  centigrade  =  degrees  Fahrenheit,     - 

1.8 

STRENGTH    OF  MATERIALS. 


ULTIMATE    RESISTANCE    TO    TENSION 
IN  LBS.  PER  SQUARE  INCH.. 

METALS. 

Average. 
Brass,  cast,        -         -         -         -         --         -         -     18000 

"      wire,  -  49000 

Bronze  or  gun  metal,          ______     36000 

Copper,  cast,        _______          19000 

sheet, 30OOO 

"       bolts, 36000 

"        wire, 60000 

Iron,  cast,  13400  to  29000,    -----          16500 
"      wrought,  round  or  square  bars  of  1  to  2  inch 

diameter,  double  refined,  -         50000  to  54000 

"      wrought,  specimens  %  inch  square,  cut  from  large 

bars  of  double  refined  iron,  _  50000  to  53000 
"  wrought,  double  refined,  in  large  bars  of  about 

7  square  inches  section,  -  -  46000  to  4700O 
"  wrought,  plates,  angles  and  other  shapes,  48000  to  5100O 
"  "  plates  over  36"  wide,  -  46000  to  50000 

Wrought  iron,  suitable  for  the  tension  members  of  bridges, 
should  be  double  refined,  and  show  a  permanent  elongation  of 
20  per  cent,  in  5",  when  broken  in  small  specimens,  and  a  re- 
duction of  area  of  25  per  cent,  at  point  of  fracture. 

The  modulus  of  elasticity  of  Union  Iron  Mills'  double  refined 
bar  iron  is  25000000  to  26000000,  from  tests  made  on  finished 
eyebars. 

Iron,  wire,  70000  to  1OOOOO 

"     wire-ropes,  -          9000O 

Lead,  sheet,     -         -  _____       33OO 

Steel,  65000  to  1200OO 

Tin,  cast,  __.._.  4600 

Zinc,  _______     7000  to  8000 

168 


STRENGTH  OF  MATERIALS-Continued. 


TIMBER,  SEASONED,  AND  OTHER  ORGANIC  FIBER. 

Average. 
Ash,  English,  -         - 17OOO 

"      American,    -  11000  to  14000 

Beech,     "  15000  to  1800O 

Box, 20000 

Cedar  of  Lebanon,   -------     11400 

"      American,  red,    -         -         -         -         -         -          10300 

Fir  or  Spruce,  -  1000O  to  13600 

Hempen  Ropes,  -        -         -  -          12000  to  1600O 

Hickory,  American,  -  12800  to  180OO 

Mahogany,  80OO  to  2180O 

Oak,  American,  white,      -          -----     1800O 

"     European,     -----         10000  to  19800 
Pine,  American,  white,  red  and  pitch,  Memel,  Riga,    -     1OOOO 

"  "          long  leaf  yellow,  -         12600  to  19200 

Poplar,     -         -         -  -       700O 

Silk  fiber, 52000 

Walnut,  black,  1600O 

STONE,  NATURAL  AND  ARTIFICIAL. 

Brick  and  Cement,     -         -  -    280  to  300 

Glass, -                                       9400 

Slate,        -  -      9600  to  1280O 

Mortar,  ordinary,  5O 

ULTIMATE    RESISTANCE    TO    COMPRESSION. 

METALS. 

Brass,  cast, 10300 

Iron,      "       -                                              -      82000  to  145000 
"       wrought, 36000  to  40000 


169 


STRENGTH  OF  MATERIALS— Continued. 


TIMBER,    SEASONED,    COMPRESSED    IN    THE 

DIRECTION   OF   THE   GRAIN.  Average. 

Ash,  American,  4400  to  5800 

Beech,     "  5800  to  6900 

Box,  10300 

Cedar  of  Lebanon,         -  5900 

"       American,  red,  -        6000 

Deal,  red,  6500 

Fir  or  Spruce,  5100  to  6800 

Oak,  American,  white,  -         -    720O  to  9100 

"     British,  10000 

"     Dantzig,         -         -         -  770O 

Pine,  American,  white,       -  5000  to  5600 

"             "          long  leaf  yellow,  8000 

Spruce  or  Fir, 5800  to  6900 

Walnut,  black, -  7500 

STONE,  NATURAL   OR   ARTIFICIAL. 

Brick,  weak,      -        -    •     -         -        -        -        -    55O  to  800 

"      strong.         -  1100 

"      fire,  1700 

Brickwork,  ordinary,  in  cement,      -  300  to  450 

best,         -  -  1000 

Chalk,  330 

Granite,    -  -         -       5500  to  11000 

Limestone,    -         -  4000  to  11000 

Sandstone,  ordinary,  ____--       4000 

ULTIMATE    RESISTANCE    TO    SHEARING. 

METALS.    - 

Iron,  cast,  -         -     27700 

"     wrought,  along  the  fib'er,         -  45000 

TIMBER,  ALONG  THE  GRAIN. 

White  Pine,  Spruce,  Hemlock,  -     500  to  800 

Yellow  Pine,  long  leaf,  630  to  960 

Oak,  European,          -  -         -        2300 

Ash,  American,     -  -  2000 


PAGE. 

Cast  iron  columns,  and  wrought  iron,  ultimate  strength  of  ____  79 

Channel  bars,  lithographed  sections  of  ...................  5-8 

"  "     explanation  of  table  on  properties  of  .......  56-61 

"  "     table  on  properties  of  ....................  64,  65 

Circumferences  of  circles,  and  areas  ..................  112-124 

Columns,  corrugated,  lithographed  sections  of  ..............  15 

"         Keystone  octagon,  lithographed  sections  of  ........  13 

"  "  "         thicknesses  and  corresponding 

areas  and  weights  ...........................  77 

"         Piper's  patent  rivetless,  lithographed  sections  of.  ...  14 

"  "  "  "         thicknesses  and  correspond- 

ing areas  and  weights  of  .....................  78 

"         explanation  of  tables  on  .....................  73-76 

"         cast  and  wrought  iron,  ultimate  strength  of  ........  79 

"         wrought  iron,  ultimate  strength  of  .......    ........  80 

"         wooden,  ultimate  strength  of  ....................  81 

Comparative  table  of  United  States  and  French,  and  French 

and  United  States  measures  .....................  166,  167 

Corrugated  and  galvanized  iron  .......................  85,  86 

Cover  angles,  lithographed  sections  of  .....................  12 

Decimal  parts  of  a  foot  for  each  •g'jth  of  an  inch  ......  ......  87 

Decimals  of,  an  inch  for  each  ^th  ................  .  ......  171 

Deck  beams,  lithographed  sections  of  ......................  4 

"  "       properties  of  .........................  .....  63 

Deflection  of  rolled  eyebeams  under  load  ...............  33-55 

"         formulas  for  special  cases  ......................  61 

Dove  tail,  lithographed  section  of  ......................  ,  .22 

Elasticity,  modulus  of,  assumed  in  tables  ..................  60 

«  "          «   for  eyebars  .......................  168 

Expansion,  linear,  of  substances  by  heat  ..................  160 

Eyebeams  ........................  «  ...........  See  Beams. 

Fence  Iron,  lithographed  sections  of.  ....  .................  22 

Fire-proof  floors  ....................................  83,  84 

Flat,  beveled,  lithographed  section  of  ..............  '.  ......  22 

Flat  rolled  iron,  weights  per  lineal  foot  of  ...............  88-93 

"       areas  of  .............................  94-99 


fit 


PAGE. 

Flexure  of  beams  of  any  cross-section,  general  formulae  on,  60,  61 

Floorbeams  of  bridges 133 

Floors  and  roofs,  general  notes  on 82-84 

Floors,  lithographed  illustrations  of 23-25 

Foot,  decimal  parts  of,  for  each  -^th  of  an  inch 100-103 

French  and  United  States  measures,  comparative  table  of. . .  .167 

Galvanized  iron 86 

Gas  pipe,  sizes  and  weight  of 132 

Gauge,  American,  for  sheet  iron Ill 

"       Birmingham,     "          " , 110 

Girders,  riveted,  table  on .' 72 

Glass,  window,  number  of  lights  per  box 159 

Grooved  irons,  lithographed  sections  of 21 

Half  T's,  lithographed  sections  of 15 

Handrails,         "  "  21 

Ice  slides,  «  " 22 

Inertia,  moments  of,  for  usual  sections 61 

See  also  tables  on  properties  of  beams,  channels,  angles,  etc. 

Keystone  Bridge  Co.'s  corrugated  iron 86 

"  "  "  standard  proportions  for  upset 

rods 126,  127 

"  octagon  columns,  lithographed  sections  of 13 

"  "  "  thicknesses  and  corresponding 

areas  and  weights 77 

Linear  expansion  of  substances  by  heat 160 

Loads  per  square  foot,  for  floors,  roofs,  etc 84 

Logarithms  of  numbers 153-155 

Materials,  strength  of 168-170 

Measures,  and  weights,  United  States  and  British 164,  165 

"  "  "        comparative  table  of  United  States 

and  French,  and  French  and  United  States 166,  167 

Mensuration 161-163 

Modulus  of  elasticity,  assumed  in  tables 60 

-_ 


PAGE. 
Modulus  of  elasticity  for  eyebars 168 

Moments,  maximum  bending,  to  be  allowed  on  pins 136 

Natural  sines,  tangents  and  secants 144-152 

Notes,  general,  on  floors  and  roofs 82-84 

Nuts,  sizes  and  weights  of  hot  pressed  square 130 

"  "  "  "          "      hexagon 131 

Obtuse  angle,  lithographed  section  of 12 

Octagon  columns,  lithographed  sections  of 13 

"  "         thicknesses  and  corresponding  areas  and 

weights 77 

Patent  post  iron,  lithographed  section  of 15 

Pillars,  timber,  ultimate  strength  of 81 

Pins,  bearing  value  of,  for  one  inch  thickness  of  plate 137 

"     maximum  bending  moments  to  be  allowed  on 136 

Pipe,  wrought  iron,  for  gas,  steam  or  water 132 

Piper's  patent  rivetless  columns,  lithographed  sections  of 14 

"           "      -       "             "         thicknesses  and  correspond- 
ing areas  and  weights  of 78 

Plastered  ceiling,  weight  of 84 

Plastering,  limit  of  deflection  to  allow  for 31 

Post  irons,  patent,  lithographed  sections  of 15 

Posts See  Columns. 

Pratt  trusses,  maximum  stresses  in 141 

"     truss,  diagram  of 26 

Properties  of  U.  I.  M.'s  eye  and  deck  beams 62,  63 

"          «  "        channels.... 64,65 

"          "  "        angle  irons 66,67 

"          "  "        tee  irons 69 

"          "  "        star  irons 69 

"         explanation  of  tables  on 56-61 

Riveted  girders,  explanation  of  table  on 70,  71 

"  "       table  on 72 

Rivetless  columns,  lithographed  sections  of 14 

"              "         thicknesses  and  corresponding  areas  and 
weights  of 78 

'< 7^ ) 


175 


PAGE. 

Rivets  and  round-headed  bolts,  weight  of 125 

Roof  iron,  lithographed  section  of 20 

Roofs,  loads  and  weights  per  square  foot  for 84 

Round  bars,  and  square,  of  wrought  iron,  weights  and  areas, 

and  circumferences  of  round  bars 104-109 

Rule  for  finding  the  area  of  a  bar  of  wrought  iron,  given  the 

weight,  and  vice  versa 84 

Sash  Irons,  lithographed  sections  of 22 

Screws,  wood 129 

Separators,  between  beams,  lithographed  illustrations  of 24 

"  "  "       weight  of 82 

Shearing  and  bearing  value  of  rivets 135 

Sheet  iron,  by  Birmingham  gauge 110 

"  "  American  "     Ill 

Sines,  tangents  and  secants,  natural 144-152 

Spacing  of  beams  in  floors 33-55 

Spikes,  wrought 129 

Square  root  angle  irons,  lithographed  sections  of 11 

Square  and  round  bars  of  wrought  iron,  weights  and  areas, 

and  circumferences  of  round  bars 104-109 

Standard  screw  threads,  nuts  and  bolt  heads,  recommended 

by  the  Franklin  Institute 128 

Star  irons,  lithographed  sections  of 12 

"        "      properties  of 69 

Strength  of  cast  and  wrought  iron  columns 79 

"         "  wrought  iron  columns 80 

"         "  timber  pillars 81 

"         "  materials 168-170 

Stresses,  maximum,  in  Pratt  trusses 141 

"  in  Whipple  trusses 142,  143 

"        explanation  of  tables  on 139,  140 

Struts See  Columns. 

Substances,  weight  of  a  cubic  foot  of 156-158 

linear  expansion  of,  by  heat 160 

Tacks 129 

Tee,  half,  lithographed  sections  of 15 

Tee  irons,  «  "  16-20 

176  * 


08 

PAGE. 

Tee  irons,  properties  of 69 

Threads,  screw,  Franklin  Institute  standard 128 

"  "  Whitworth  standard 129 

Tie  rods,  for  brick  arches  in  floors / 83 

Timber  beams,  safe  load  for 138 

"  pillars,  ultimate  strength  of 81 

Tubes,  wrought  iron  welded,  for  gas,  steam  or  water 132 

Upset  screw  ends  for  square  and  round  bars 126,  127 

Weights  of  a  cubic  foot  of  substances 156-158 

angle  irons,  corresponding  to  thicknesses  vary- 
ing by  TV'-. 68 

"          brick-work,  walls  of 83 

"          flat  rolled  iron 88-93 

nuts,  hot  pressed,  square  and  hexagon 130,  131 

"          separators  and  bolts 82 

sheet  iron 110,  111 

"          square  and  round  bars  of  wrought  iron 104-109 

tubes,  of  wrought  iron,  for  gas,  steam  or  water. .  .132 

wrought  iron,  rule  for  finding,  given  the  area 84 

"        spikes,  wood  screws  and  tacks. ...'.....  129 

Weights  and  measures,  United  States  and  British 164,  165 

"          "  "          comparative  table  of  United  States 

and  French,  and  French  and  United  States 166, 167 

Whitworth  standard  screw  thread. 129 

Window  glass,  number  of  lights  per  box 159 

Wooden  beams,  safe  load  for 138 

Wood  screws 129 

Wrought  spikes 129 

Z  iron,  lithographed  section  of 22 


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